Don't characters fall out of elite anymore if you don't play them?
Is there some pre-requisite I don't know about?
GSP is just an abstraction of your rank. It's still pretty much first, second, third, etc, just has Smash's own twist to it. As more people buy the game and/or play online for the first time, the GSP cap will grow and move everyone up relative to what rank they had before. So you'll still be say "33rd" your GSP will just move up with the new players entering, bringing you from say 3,555,630 to 3,557,436. Your overall position will still stay the same, just the numbers will go up to reflect the new overall GSP amount, stemming from the new players joining.
So your "real" rank doesn't actually go up or down solely from new players joining. What does, is other players doing better relative to you. People "fall out" of Elite Smash due to other players of that character winning more games than you. And some people can stay relatively the same despite not playing that character for a long time, because they happen to have a really high rank that other players can't achieve.
For example, my Ness has fallen out of Elite before and required me to go and "touch up" on him. I didn't get very far into Elite with Ness, so it's not surprising it didn't take long to "fall out" with such a popular character. In contrast, a lot of my other Elite characters have stayed roughly the same, because I got pretty deep into Elite with them and there aren't many players who can reach that high to usurp me.
Edit: Oh and the prerequisite to getting to Elite is simply passing over a certain GSP threshold. What that is currently I don't know though, I don't play online much anymore and don't have many characters at that level.