OH, ... make doubly sure the circuitry around the '1307 is right. IIRC, it's easy to accidentally end up with the backup battery trying to power the rest of your board when you pull the mains plug. That inevitably drags the backup voltage down to zero even if you've got a good battery.
In particular, make sure your grounding and decoupling is good. If your ground line goes missing or (has nonzero impedance during transients), that can cause supply issues at the chip too.
If you're powering directly from a wall-wart, unplug it from the board instead of from the mains supply. Otherwise, the large capacitors in the brick will slowly discharge into your circuit, causing an extended brownout.
$0.02.
b.g.