Yeah, clock generators are wear items, but they don't wear out THAT quickly. Chances are that it's the CMOS battery. It's an extremly unlikely event that it could be a short, especially if you haven't done anything to it, and that's really the only other thing that I can think of.
I've only seen clock generators go bad a couple of times. Both times they had an insane amount of voltage on them (way out of spec for these particular ones). They ran faster, then when the correct voltage was used, they still ran faster.
If you have access to an oscilloscope at your house, hook it up.
If not, or you don't want to spend a lot of time with it, just get a brand new battery from Bartell's or Radio Shack. They're the same batteries used in watches and calculators.