I think I have a similar problem. Usually, I can only come up with new character ideas when I really, really don't need them. When I do need one, either nothing comes out or I easily come up with shallow characters that quickly grow boring and are replaced by similarly boring replacements. This is especially problematic in new games.
I've found I can usually create characters that survive longer if I create them with other characters in the game in mind, or with a really god plot hook. This works best if the other players can roleplay well, or if your DM can fit your plot hooks into the campaign (or, all things considered, help you use an existing hook of the campaign into a drivng force for the character).
After that, what ranger89 says is absolutely right. Thinking of your character as a bundle of statistics (race, class, skills and feats, etc = all stats) is a quick way to lose interest. It's not the same as true optimization, but it does sound like you get lost in the stats.
EDIT: Aditionally, I'm sure that if I were limited to only one PC at a time in my games, I'd have even more trouble. Fortunately for me, the way my group plays we almost always have more than one PC in play at a time.