It depends, really it does. On the author, on how interested am in what fandom(s) they move on to, on my mood at the time. And sometimes you get hooked on a new fandom as a result; I got hooked on Buffy in 2003/4 after the last episode was aired, solely because of fanfic, and I can't even remember at this point what author it was that made me start reading it. And now I own the first three seasons on DVD. I didn't like the movie "Labyrinth" when I saw it, but I do read the occasional Labyrinth fic because a favorite author of mine wrote one and I liked it.
But losing authors isn't what you should be worried about. It's losing archives. Because when the main archive for your fandom/pairing (or even just the archive that you like the best) goes the way of the dodo, it can be very painful. Because inevitably there'll be a few fics that aren't backed up anywhere. Your fandoms are all ones that are still active fandoms; as the show gets canceled, they tend to become less active as a general rule. As that happens, as people move on to other fandoms or out of fandom in general, it becomes harder and harder to find people willing to go to the effort of maintaining the archives.
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But losing authors isn't what you should be worried about. It's losing archives. Because when the main archive for your fandom/pairing (or even just the archive that you like the best) goes the way of the dodo, it can be very painful. Because inevitably there'll be a few fics that aren't backed up anywhere. Your fandoms are all ones that are still active fandoms; as the show gets canceled, they tend to become less active as a general rule. As that happens, as people move on to other fandoms or out of fandom in general, it becomes harder and harder to find people willing to go to the effort of maintaining the archives.