How do you get Inspired / re-Inspired in a Game?
Like donsr said, it's a good idea to know what your limits are. For me, I know I can probably run one game at a time and give it my full attention, and problems arise when I add another game or two to that load. For playing games, probably six at a time is my max.
I typically don't drop out of games due to boredom. When I drop games, it's usually because I've let myself get too busy offline and don't communicate properly to my GMs or players. I've stuck with games for years when I didn't feel especially inspired, but if I stick with it, sooner or later that spark will return.
Once it was down to only having two players still with me, but one player was excellent and really rewarding to play with, and the other player was game enough to keep posting, and we were able to finish at least the current adventure we were on.
What keeps me engaged as a player is having meaty, interesting adventures to play in filled with description, exploration, choices, and consequences. I've played with some excellent GMs who really put care and time into their games to create living, breathing worlds for the players to explore, and these GMs typically only run one or two games at a time.
It's important to be honest with your players and GMs, too. Check with them periodically to find out how invested they are in the game. Often I find players' motivation to continue can be infectious to make me want to continue. It's good to let GMs know when you're enjoying their games. They may be wondering if anyone's still invested in that game.
And as donsr said, it's important to run games that you're interested in. If you're thinking about starting a game, but the game doesn't interest you, you probably shouldn't start it. It's hard to manufacture enthusiasm for something you're not that interested in.