Contested Sequel: With the exception of A's, which is considered an Even Better Sequel, any other entry into the main continuity has left the fandom polarised. It doesn't help that the author is constantly tinkering with the established formula in very unsubtle ways.
Magical Girl Lyrical Nanoha Strikers caught flak for having a 10 year timeskip, thus losing most of the lolis. It moved the setting away from Earth and shifted focus from the previous main characters - demoting several to extras in the process - to a bunch of rookies and a lot more non-essential background characters. The Numbers cyborgs probably got the most heated debates among the fandom as to whether they were credible antagonists compared to the very powerful rivals from seasons one and two. They were also not as well-developed as previous antagonists, probably because there were so many of them. The third season was twice as long as previous seasons, but rather than using that extra time to develop its enormously expanded cast or give screentime to those characters inexplicably shoved out of the picture, the writers instead devoted most of the episodes to training the newbies and discussing military policies.
Magical Girl Lyrical Nanoha Vivid was the first installment to shift from anime to manga, and a monthly one at that, so it already had a strike against it before it even started. Then it turned out it was a Lighter and Softer take on the series with plushy devices, no interdimensional incidents, Magical Girl tropes played straight and more lolis and loli fanservice than ever. It actually reads more like a shonen series with magical girls... and no real antagonists. And then it put the breaks on whatever plot it had going to do a lengthy Tournament Arc and introduce a bunch more new characters. People who liked the changes in StrikerS were disappointed, but in Japan where moe is the law it's the most successful entry in the franchise yet.
ViVid Strike! send waves throughout the fandom with it's very announcement considering the fact that it's a sequel to Magical Girl Lyrical Nanoha Vivid (which as previously stated is a Contested Sequel in its own right). It also didn't help that, at the time, the third Nanoha movie was still in limbo which angered more then a few fans. Things got even worse when it was seemingly confirmed that, much like StrikerS Sound Stage X above, it was a sequel using only new characters and ones introduced from Vivid meaning no Nanoha or Fate (which also makes it the third entry in a row without the two as main stars). Now that the series has finally been released initial reaction seems to be split between those who like the new characters and appereciate the Deconstruction of some Nanoha trope stables or others who are sick and tired of the franchise no longer being about Nanoha and have no interest in the series.
All of this is just from the main series. If we add the alternate continuities, we can also mention:
The Movie 1st, which was accused by some of being an unoriginal rehash of season one with half the plot and twice the explosions and cutting out pretty much anyone that wasn't Nanoha, Fate or Precia. Others liked it for exactly the same reasons.
The Movie 1st manga, which later turned out to have little to do with the movie and more in common with the light novel. It was widely decried for the perceived change in character of Nanoha - or Emoha as this version is known to the western fans - and generally trying to be too dramatic with the brutal fight scene between Nanoha and Fate that lasted for most of the second volume. And despite being an Alternate Universe that changed many things along the way, it still ended the exact same way as the original anime and the movie, leaving many to wonder what the point of it was.
The Movie 2nd A's was accused by many of butchering the lauded A's storyline. People complained about the changes such as: replacing Nanoha and Fate's reunion from Big Damn Heroes to hugging; having them completely defeated in the first encounter with the Wolkenritter; removing Yuuno from the battle; teasing a fight scene with Lindy that gets promptly aborted; Reinforce trying to kill Fate and Nanoha, without a good reason this time; Nanoha doing significantly less well against Reinforce; and of course, removing the Liese twins and the Graham subplot altogether.
The Fate/stay night crossover, which disappointed people who were expecting something serious and longer than a one-shot.
The Battle of Aces was generally well-received for shifting the focus back to the A's characters and the introduced Evil Twins of the main characters became popular enough to be included in the sequel, but even most of its fans admit that it was mediocre in terms of gameplay.
The Sequel to the above game The Gears of Destiny almost broke this trend. The game have a stronger AI, great amount of playable characters, and a good story with good character development. However the manga cast contributed next to nothing to the overall main story, and the ending used Laser-Guided Amnesia and removes all the Original Generation characters from the timeline until at least Magical Girl Lyrical Nanoha Vivid. It feels like they were trying to invoke In Spite of a Nail to make this timeline identical to the main one. It left the feeling of The movie manga all over again.
Ensemble Dark Horse: Despite suffering of Chuck Cunningham Syndrome, Yuuno is pretty popular by the fans, as he often appears in many fanarts and fanworks. In the latest popularity poll of ViVid, Yuuno manages to get the 13th place despite appearing only in a single panel.
Friendly Fandoms: Fans of Gundam have been noted to enjoy Lyrical Nanoha. The fact that many character designs are Shout Outs to various Gundum designs and the main characters shot giant laser beams at each other that wouldn't look out of place in said Gundam shows naturally help.
Hilarious in Hindsight: Would you believe this was the prototype for the series? If you've watched the show for any length of time, the sight of Nanoha waving around that puny heart-shaped wand alone will be enough to make you crack up.
Just Here for Godzilla: Subverted. Before the first season's Growing the Beard moment, viewers were expected to just be there to see cute little Nanoha from Triangle Heart 3: Sweet Songs Forever in a strange alternate universe. They were quickly disproven when Nanoha got more viewers than the Triangle Heart 3 OVA. Ever since Nanoha became the perfect example of More Popular Spinoff, to the point where anyone looking for Triangle Heart 3 is probably just there to see Nanoha in a strange alternate universe.
Due to her Love Martyr status and stubborn refusal to hold any kind of ill will towards her abusive mother, Fate is often portrayed as a memetic masochist who loves to be wiped, electrocuted and generally punished. Needless to say this fits well with the merciless White Devil flanderization of Nanoha.
Due to her whole Defeat Means Friendship shtick, "befriend" has become an euphemism for "beat the living crap out of".
Rescued from the Scrappy Heap: As time passed, reception of Precia Testarossa has lightened, especially in presence of the much reviled Hückebein. First she got Woobie moments in the Movie 1st, then in Gears of Destiny her spirit made peace with Linith's, and finally INNOCENT showed what kind of mother she would have been had she not lost Alicia. Impressive, when back in the day, she really was the bonafide "most despicable, worst mom ever" with evil acts to prove it.
They Wasted a Perfectly Good Character: YUUNO. In a series so focused on how the ancient civilizations and technologies of the past are enormously impacting upon the present day, having an archaeologist, scholar and librarian of ancient knowledge in the cast would seem like a great idea. If nothing else, Yuuno could have continued his role as Mr. Exposition in Magical Girl Lyrical Nanoha Strikers, Sound Stage X, ViVid and Force, considering that no one would be better qualified to explain about the Belkan Reunification War, the Sankt Kaiser dynasty, the Saint's Cradle, the Hegemon Klaus and his relationship with Olivie, Queen Ixpelia and the Mariage, and perhaps even the Bible of the Silver Cross and its Eclipse Virus.
Also the children are superpowered. One could argue they need to be given something useful to do, lest they find their own trouble, also that they're not in much danger; alternatively, there's so much danger to entire cities or even planets that you have to use every resource you can. Sound Stage X refers to a planet with 'real' child soldiers with guns, and IIRC that's portrayed as messed up and tragic.
More dissonance: not only is Chrono a 14 year old military officer (again, with the powers of Starman), but his mother is his commanding officer.