Fullmetal Alchemist: Unbelievably this happened to a dozen of Roy/Riza doujin circles during the Briggs Arc, when their OTP went out of focus after the Ishval memories chapters; while said chapters also had their own effect in driving away some of the fans who were more for the standard office romance. Recently, the series finale didn't help, either.
Mahou Sensei Negima!: Negi/Asuna. Between the fact that their relationship works fine non-romantically, rival ships (like Nodoka, Kuu Fei, Yue, Ako, Makie, Luna aka Shiori, Fate, etc.), and the false revelation that Asuna is Negi's aunt, though debunked by the fact that she is way too old, somewhat reviving this ship with minor Tenchi-style family confusion.
Paradise Kiss: During the first volumes, Arashi Nagase and Miwako Sakurada attracted massive amounts of shipping. However, as the series progressed, readers tended to gradually back away from the (canon) ship, as Arashi's attitude towards Miwako started to become aggressive and sometimes violent, and then came The Reveal that he raped her during their first time. Even though Miwako doesn't hold it against him, Arashi feelsveryguilty about his behaviour, and tries to correct what he has done. Despite this, the fact that they end up together and even have a child has proven too squicky for many fans to overcome.
Revolutionary Girl Utena: Many fans dropped Mikage/Mamiya (the show's first canonically gay couple) when it turned out that Mamiya was an illusion acted out by Anthy, a girl. Even without the Het is Ew aspect, the fact that it was all an elaborate ploy by her brother Akio to make Mikage an Unwitting Pawn was also more than enough for the ship to be abandoned.
Tsubasa: RESERVoir CHRoNiCLE: What had been a very vocal group of Fay/Chii Shippers (in contrast to the majority of Kurogane/Fay shippers) mysteriously disappeared after it was revealed that Fay had based the design of Chii off of his late mother. Apparently this was enough to turn most, if not all, of the Shippers away from the pairing (and the former Trope Namer comes from the reaction of a poster on an internet forum.) There was also the small fact that Chii disintegrated after the Feather used to create her was removed, and that probably put a major damper on the idea of them being involved in the future.
And then cue the revelation that Syaoran is really actually the son of his own clone and his Sakura's clone, not the CCS pair. Fans are abandoning ship left and right, although there is a fair bit of confusion about which ship to abandon.
Quite a few other people bailed on the pairing after Saito tried to have sex with Louise while she was asleep.
ElfQuest: Ember hooked up with Mender once she reached puberty. The fandom generally liked him until he went off to fight in the war and was replaced by Ember's second love interest, Teir - who came literally out of nowhere. Now, the original authors and the guest artists/writers alike all collectively prefer Teir over Mender now... the fandom, predictably, is much more split on the subject, evenly between forgetting Mender even existed, and seeing Teir as an abhorrent Creator's Pet.
X-Men: Scott Summers has a rather unfortunate history with women. Scott/Madelyne lots all support when Jean Grey returned from the dead and Cyclops left his family with Madelyne and his newborn son Nathan to be with Jean again, an event that was responsible for the Inferno tragedy. Then in Grant Morrison's New X-Men Scott/Jean fans dropped Scott like a bad habit after Scott began an affair with former nemesis Emma Frost that that was ultimately solidified when the 2 made out on newly deceased Jean's grave. During Avengers Vs X-Men, Scott/Emma fandom took a heavy 1-2 blow when Emma revealed her affair with Namor and Scott choking out Emma to gain her half of the Phoenix Force.
Star Wars: Despite it coming out of nowhere and being obvious in its intentions, the revelation that Luke and Leia were siblings did kill off the fandom (and there was a fandom after the first two movies)... for a while. Since then they've grown up and have resumed shipping them.
Early on, the Wreck-It Ralph fanbase shipped Ralph with Vanellope. As it turns out, Vanellope is a cute little nine year old girl. The fanbase immediately stopped shipping them and instead preferred a big brother-little sister, or even father-daughter, friendship.
After the events of the book, previously vocal Harry/Cho Shippers appeared to Evanesco.
It also saw the once-popular Percy/Penelope ship (it had the advantage in the early days of being the only canonical ship whose characters weren't old, dead or both. For a time, it was probably the largest ship not involving some permutation of Harry, Hermione, Ron and Draco.) dwindle away to virtually nothing, for a different reason. J.K. Rowling later stated in an interview that Percy went on to marry a woman who was not seen in the books, which killed off a lot of the remaining shippers.
Tortall Universe's Song of the Lioness series. An example of an Abandon Shipping that took place within the story itself occurred when Pierce realized that her planned ending of Alanna marrying Prince Jonathan wasn't really what Alanna wanted and wrote them breaking up after Jonathan proposed to her. Instead Pierce paired Alanna off with her Gentleman Thief friend George Cooper and introduced Rebellious Princess Thayet for Jonathan.
Warrior Cats: Many shippers abandoned Whitestorm/Bluestar when it was revealed that he was her nephew. The ship was even dubbed 'Denialshipping'.
In the Smallville fandom, the earliest handful of episodes saw Clana (Clark Kent and Lana Lang) enjoy a majority of fan support, but as Lana became increasingly unpopular, the Clana ship went from being popular and accepted to being the least shipped relationship (and undoubtedly the most hated) within a mere two or three years.
Chlex (original character Chloe Sullivan being paired with Lex Luthor) used to be a fairly popular pairing, often accompanied by tons of Draco in Leather Pants for Lex in fanfics. However, after the events of "Freak," the episode where Chloe is revealed to be a mutant and Lex orders his scientists to kidnap her and perform sadistic experiments on her, before almost killing her, most of the shippers quite understandably lost their taste for Chlex, as Lex had proven himself to be too much of a sociopath for even Draco in Leather Pants to make the ship popular anymore.
Also, many former Clark/Chloe shippers moved on to shipping Clark with Lois Lane once she arrived on the scene, and many more switched to Chimmy (Chloe and Jimmy Olsen) and Chlollie (Chloe and Oliver Queen) by the end, though there of course many continued to ship Chlark.
Battlestar Galactica: had this happen to Kara/Lee mostly after the fans found the pair's actions in regards to their spouses during the Quadrangle of Doom despicable. Attrition though took place throughout the whole series with fans jumping ship as early as the first season finale, by the series finale Roslin/Adama overtook them as the largest ship in the fandom.
Dollhouse: More than half of Topher and Claire's fandom abandoned shipping when it was revealed that Claire was actually a Doll and claimed she hated Topher's guts. Those who left began to ship Topher with Adelle, until Bennett came into the picture and killed whatever was left of both pairings. (Before, you know, getting killed off by Claire...)
Friends: The Ross/Rachel ship was popular when the show started, but much of the fandom tired of the pairing somewhere around the end of season 3/early season 4, prefering the more stable Chandler/Monica ship. The writers annoyingly remained hooked on the R/R ship, keeping the Unresolved Sexual Tension drawn out for the rest of the show's run, with Word Of God even later admitting that whenever there weren't any major relationship-related plots going on they could always bring out another airing of "Ross and Rachel", believing this to be what the fandom wanted.
Heroes: The Reveal that Peter and Claire are related did scare off most of the more casual 'shippers. However, many stuck to it, either pretending that the reveal didn't happen or just accepting it regardless. Considering that the fandom's most popular Ho Yay pairing is Peter and his brother, this isn't too surprising.
There seems to have been a significant drop in Mohinder being paired with anyone ever since his experiments with Super Serum kicked off a mutation into... whatever the heck it is he's turning into.
iCarly: The Seddie (Sam/Freddie) ship seems to lose shippers every time Sam ups the Comedic Sociopathy against Freddie or she bumps her Moral Event Horizon. Examples include throwing Freddie out of a treehouse after delivering to him a harsh beating with a tennis racquet in "iMeet Fred" and running a child labor sweatshop during "iSell Penny Tee's."
As with many pairings that get together and then break up later, there are fans who abandoned Seddie after their break up in iLove You. Either through having seen the relationship and not be satisfied with it or because they were satisfied by what they saw and wanted the show to go back to being about comedy.
LOST: A decent amount of shippers in the fandom jumped ship when it was revealed that Jacob and the Man in Black are twin brothers. Others have continued to ship it.
Although there was Ship Tease between Arthur and Morgana in the first series of Merlin, many shippers soon lost interest simply because they barely interacted in series two, and were then revealed to be half-siblings in series three (and still didn't interact in any meaningful way). Despite the potential for Foe Yay, they only had one brief scene together throughout the entirety of series four.
Robin Hood: The Sheriff/Guy ship seems to have died out in series three after Guy attempted to kill the Sheriff and later had a Heel Face Turn ... then the Sheriff killed him in the final episode. He joins the outlaws around the same time that his sister Isabella does a Face Heel Turn, which put off a lot of people who were beginning to ship Robin/Isabella.
However, the fact that Guy of Gisborne deliberately murdered Marian by impaling her on a giant sword didn't deter the shippers in the way that the writers apparently wanted it to.
Stargate Atlantis, once it was revealed that Teyla was pregnant with the baby of her fellow Athosian, Canaan, and after the child was born, many dropped all ships between her and anyone else.
Though the idea that a relationship could've taken place before her relationship with Canaan allows many ships to stay afloat, including but not limited to Sheyla (Teyla/Sheppard, the most popular pairing involving Teyla), Teyla/Ronon, and even McKeyla (Teyla/McKay, due to McKay, oddly enough, being the series' Launcher of a Thousand Ships).
Stargate Universe: the Eli/Chloe ship was already on life support by Season Two, but the arrival of Ginn put the nail in the coffin.
Star Trek: Enterprise: During the first couple of seasons all signs pointed towards a ship between Captain Archer and T'Pol, until the third season when all of a sudden the ship turned into one between T'Pol and Trip Tucker.
With the series finale bringing back the idea of a T'Pol/Archer pairing.
Kamen Rider Den-O appeared to have quite a bit of ship tease between Ryotaro and Hana, until Hana's actress left the show and the character reverted to her ten-year-old self, "Kohana." However, Ryotaro/Hana remained popular in fandom until the reveal that Hana was Ryotaro's niece; fans jumped ship abruptly.
Kamen Rider Kabuto has a similar example whereby Tendou was commonly shipped with Hiyori, until the show revealed that she is actually a Worm based on his sister. Whatever shippers were left after that ( since she's technically just a copy of his sister, not the actual one) drifted away or jumped ship after the God Speed Love movie made her the girlfriend and later wife of Kagami.
Doctor Who fandom saw a marked drop-off in the number of fics where River was paired with Amy and/or Rory after the reveal that she's their daughter.
It did a fairly good job of killing Doctor/Amy/Rory too, which, as you can probably guess from the way it's that trope's page picture, was previously pretty popular.
Prior to Amy and Rory getting married and Rory coming back into existence, there was also intense Doctor/Amy shipping (the ending of Flesh and Stone didn't help matters).
Mickey/Jackie, formerly a popular ship mate to Tenth Doctor/Rose, has pretty much died off since the pairings of Jackie/alternate Pete and Mickey/Martha became canon.
Doctor/Rose shipping did reach a height towards the end of Season 4, until Journey's End closed that door forever by pairing Rose off with the Doctor's clone instead.
A lot of people(thought not all) backed away from the once golden couple Chuck/Blair on Gossip Girl after the start of season 3, thanks to Chuck whoring Blair out to his uncle Jack in "Inglourious Bassterds".
Apollo Justice: Ace Attorney, Trucy and Apollo tend to gather shippers early on in the game due to their quirky antics and how they team up to solve cases. However, at the very end of the game it is revealed that Trucy and Apollo are in fact SIBLINGS, thus causing many fans to reject the pairing. To add insult to injury, there's also the fact that Trucy and Apollo are never seen learning the truth of their heritage, leading some to worry that they NEVER find out, and maybe DO attempt a relationship anyways!
Heavy Rain: Scott Shelby and Lauren Winter. All gone to hell when it is revealed that Scott was the person who killed Lauren's son. She whacks him in the most epic way though.
Shadow Hearts Covenant: Aw, Yuri and Karin make such a cute couple. Oh, wait. She's his mother!? Icky! Wait, how does that work? Stupid time paradox!
Tales Of Symphonia: Kratos/Lloyd was looking good for most of the game. From Lloyd's jealousy of Kratos's strength, and Kratos's efforts at training and defending him, the strengthening of their bond while they traveled together, and Kratos's obvious desire to protect Lloyd (and Lloyd's equally obvious desire to trust him) after Kratos's Face Heel Turn, the connection was obvious and easily made. ...Then near the end of the game, it turns out that Kratos is Lloyd's father.
The World Ends With You: Some people began to ship Beat and Rhyme due to their close interactions at the beginning. This was quickly dropped by most when we found out that they are siblings. And that Rhyme is SUBSTANTIALLY younger than Beat. But...
The Girl Genius fandom had a variant, in that shippers didn't ditch a pairing due to one of the characters doing something unconscionable, but simply because a better one showed up. When Tarvek and Bangladesh interacted, Bang's schoolgirl glee at seeing Tarvek again earned the pairing a lot of fans. Two days later, Bang met Vole, and everyone immediately jumped to that ship. To quote one of the posters on our own forums: "I support this ship. I support this ship so much it will not displace water. I support this ship so much it will be a skyship."
When it was revealed in Homestuck that Dave/Rose and John/Jade would be incest because those pairings are siblings, the ships dropped off the face of the internet. They do still exist to some mild extent, but the addition of many new characters since then such as the Trolls has made such pairings irrelevant.
There is a major subversion however. John has directly stated he's not interested in men, and later said he wasn't interested in any romance at all. John/Karkat and John/Dave remain probably the two most popular ships in the series.
Around this same time, it was revealed that Louie, Ian, and Gino were all related (Louie and Ian are brothers, and they are both Gino's half-brothers). Upon this revelation, those that shipped these three in some form or way eventually abandoned ship.
Batman Beyond: Terry/Bruce was a big favorite for fans. The way they were presented you'd think they were perfect....until JLU Epilogue came out and well, turns out Bruce is Terry's biological father and.... Well the pairing is now very rare. Actual incest is something that makes even Batslashers uncomfortable sometimes.
Out-of-universe, many Duncan/Courtney fans abandoned ship after Courtney became a Jerk/Villain/God Mode Sue in TDA, most switching to Duncan/Gwen. Her personality improved in season three, but it didn't stop the D/G Relationship Upgrade.
The Legend of Korra might set a record for turnaround time for a ship being created, then abandoned:
A promotional poster for the show distributed at ComicCon 2011 featured Korra with an Earthbender boy and a Firebender boy. Naturally, some fans started Ho Yay Shipping them right away. Later, during the panel for the show, it was revealed that the boys were siblings, and everyone not into Incest Yay Shipping jumped ship.
When all that was known about Meelo was that there was a character with his name, people thought he might be Korra's Love Interest. Needless to say, when he turned out to be a toddler, that thought died out completely.
Tenzin and Korra. They were the first two named characters and were paired up almost immediately in a Mentor Ship... until it was found out that Tenzin was a married man in his fifties with three kids and a pregnant wife.
That same barrier, however, has done nothing to sink the Tenzin/Lin ship. In fact, it may be the Linzin ship’s impossibility of ever sailing again that has fueled its voyage through the hearts of the fandom.
Furthermore, Tenzin/Pema was shipped by nearly everyone until Lin's past relationship with Tenzin was revealed. As one fan said:
They did it. They actually did it. Bryke killed the show's one otp.
And Amon/Tarrlok gained a small Mind Game Ship / Foe Yay following after Amon de-bends Tarrlok in a fairly Ho Yay-tastic scene, only to fall into this trope once it's revealed they're brothers, meaning that anyone who didn't like incest jumped ship, and resulted in a few Hilarious in Hindsight pieces of fanwork before that particular revelation.