I haven't checked my Silver or Crystal games, but I know that the clock got screwed up somehow on Gold (see the "'TIME NOT SET'?" thread if you want more details). I still haven't decided whether or not to risk resetting the clock, so I'm not certain if the game's screwed up for good.

If it's a battery problem, and if for some reason you really want to avoid losing your data, you could try finding a place that'll replace the internal battery. But I don't know if anyone would be able to do that, and that might not be the problem with yours, anyway.