Re: System Time Not Updating
A bit more information would help. Are you running a custom ROM/kernel? If so, I'd suggest re-downloading and re-flashing. I'm going to assume, however, that you're for all intents and purposes running a stock device seeing as you didn't mention such customizations. Even running stock, it's likely a software issue; it is possible that it is a network problem, though less likely. It's unlikely to be the result of a third-party app (this statement is not necessarily as valid for apps which take advantage of root access).
Originally Posted by badmf222
Again, the most straightforward solution is a full reset. Back things up with the always-helpful Google account, do a full reset, and finally add your Google account and let everything re-populate. If you are indeed running stock -- and the problem persists after going through the paces of a reset -- it's time to look at the possibility of a hardware problem, and if that has no success, a network issue.
Edit: I should mention that I have encountered this problem before, twice. In one case it was a software issue. In the other, it was a network issue, but it's highly improbable that the circumstances under which it occurred would be present in your case.