This is a good example of the dilemma anyone fixing an electronic product
faces -- do you want to find out exactly what's wrong, or do you just want
to get it working again?

My own bias is towards the former, but eventually one has to stop
experimenting and "fix the damn thing, already".

Given that it's battery-operated, a thermal problem seems unlikely. A bad
solder joint, or a cracked trace or solder pad seem likely. It might also be
a bad transistor.

I would unsolder all the components around the suspected-bad area, and
troubleshoot for a cracked trace/pad. If you can't find any, replace all the
unsoldered components with new ones.