What can I expect from my ATmega328 when the batteries run down?

UPDATE: The batteries ran down below a level that was acceptable. They lasted about 10 hours. Incorrect time digits were being intermittently displayed. So now I know.

I put in some fresh batteries and all was well. But for now I've hooked up a 5V wall-wart and am running fine. I don't think batteries are going to be a viable power option, unless it's for a quick demo when I don't have access to AC power.