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Let's face it, you've seen at least a few fanfics that are amazing, but are dead or have updates that become more and more infrequent as time passes. The reason for this is pretty simple: Fanfiction writers have no incentive to work beyond their own personal enjoyment. There is no reason for them to keep writing if they lose that enjoyment or no longer have the inspiration or free time to work on it.
Subverted with You Got HaruhiRolled!. In its first year there were 81 chapters written (that's one update every four days or so, for the curious) and since only three chapters have been released in its second year one could be forgiven for thinking that a major Schedule Slip has occurred. But in fact, the creator hasn't stopped writing; he has simply updated all of his short and mid-length chapters in a Spin-Offfic while reserving HaruhiRolled itself for his longest work. Taken together, he still averages one chapter per week.
Unfortunately, since March of 2012 this has been Double Subverted, due to the author's college schedule getting in the way of updates of any sort. There has only been a single update since then.
This happened to Harry Potter and the Methods of Rationality. Around Christmas 2011, nearly four months after Chapter 77 was published, Chapter 78 was finally done, but to spare the readers the nerve-wracking wait between its cliffhanger and Chapter 79, the author decided to finish Chapter 79 first. When that one was finished three days later he then decided to finish the whole arc first because his speed had improved so much.
But three weeks later, he was already finishing chapter 81 and explaining that he was still making backwards edits to all the unposted chapters. So most of the complainers have stopped complaining and asked him to just post more often on his progress.
Season 5 (retroactively named Part 1) was very slow with uploaded "Nocturnals", sometimes getting a bi-yearly schedule, but garfieldodiesaved it by uploaded the rest of the stories as Part 2, explaining that the delay was because of real-life issues.
The Naruto fanfic Team8 was not updated for a period of over two and a half years, from when Chapter 21 was posted in January 2011 until Chapter 22 was posted in September 2013, and has not been updated since then.
In Opening Dangerous Gates, around April/May 2014, the author's stored notes and outlines were deleted by a computer failure. She assured that she is not giving up on the story and must simply write them over again, but warned the readers that updates will not happen as frequently as a result. She later explained that she has to focus on college.
The highly popular /r9k/Elsa Is Suffering (a modern retelling of Frozen) stopped at 41 chapters for five months. Many fans became convinced that the story had been scrapped, only for the author to publish the final three chapters together on July 22, 2014.
Thoroughly averted by Ocadioan'sInheritance Cycle fanfic series "A dance of Shadow and Light". It spanned 2 years, 4 main stories(and 1 set of sidestories), 600k words and every single chapter was on time in an already explained schedule, to the point of the author even apologizing once for being 5 hours late(and uploading chapters earlier if he thought there was a good chance of him not being able to do so on the specified day). Not to mention the Reference Overdose that probably took way more time to figure out.
The "Frozen" fan fic, "The Sting of Summer's Winter" has not seen an update since September 7, 2014. Now, at the time of this writing, the author has stated that she would like to finish the story by New Year's Day, but it remains to be seen if she can follow through with this statement. If she does finish by her target date her story will not have been updated in over three-and-a-half months, this is an oddity because "Sting" updated on a fairly consistent basis of every two to three weeks before its current schedule slip.