DS1307 battery question

[vulture2600]

Has anyone had any experience with a DS1307 and an older battery causing a sketch to hang and require a reboot of the arduino at seemingly random times?

I've been having problems with my thermostat that I've been working on for a few years. It will hang and become unresponsive and require the reset button to be pressed.
On a whim, I replaced the battery. I havent tested the old one but if a battery gets low, even with no power loss to the main board, can weird things happen and hang the main board?

I can post my code if necessary but it's long and the RTC code has always worked fine.

Thanks in advance!