I've noticed both of these problems as well. There's not really anything you can do about the rubber bands, because the black ones are crap. If you want to replace them, use some spare white/red ones as BigBen suggested.
And the stickers on my original AT-TE are crumbling and to the point where they'll be gone soon too. I don't think playing with the set affects it too much (as I did when I was young), just so long as your carefully not to abrade the stickers. If you didn't apply them really well on a clean, smooth surface, that could definitely contribute to their falling off. You also have to be careful that the stickers were applied evenly and with no creasing, or they will fall off very quickly. It's all about how careful you were with application--I have some sets displayed in the sun, on an open shelf (stupid, I know, but the only place I have left to store anything...), and the stickers on that are fine, just as good as the day they were applied several years ago.
I am the brain, that which keeps you sane
I think your thoughts, I feel your pain
I am able to control both body and soul
I am never asleep, and I make you whole.