Sometimes, fanbases are, or appear to be, perennially complaining not just about minute details of the Canon, but about everything. This sometimes relates to fake fannishness: some people just don't like a piece of fiction, yet insist on consuming it. It's not just Snark Bait, it's just some people who call themselves fans but think, "Well, those new additions aren't very good. But, then again, it wasn't very good in the beginning either."
A possible sign of an Unpleasable Fanbase is a Morton's Fork: if they complain about one thing, and the people behind the franchise listen and fix it, only to have other parts of the fanbase complain about the change. This is because, in extremely large fandoms, different portions of the fandom complain about distinctly different things, so that any change (and in particularly bad cases, any lack of change) will inevitably anger someone.
Basically, this is about a fanbase which is so varied and divided in opinion that it's impossible to give everyone in it what they want.
While Unpleasable Fanbase has been a problem for any media with a sufficiently large fanbase (you simply cannot please all of the people all of the time), in the Internet Age it takes on a new dimension when even a small minority can make their opinions heard. It's enough to make an author want to give up.
See also Accentuate the Negative, Contested Sequel, The Law of Fan Jackassery, Ruined FOREVER, Fan Dumb, They Changed It, Now It Sucks!, It's The Same Now It Sucks, Complaining About Complaining and Why Fandom Can't Have Nice Things. When the creators announce something that actually does get the fandom in line with them, it's And the Fandom Rejoiced.
No examples needed. The specifics of fan complaints really don't matter, here. It's always something.