I bought a new aftermarket battery (couldn't find a Nokia one, and given that it failed, not sure I want to). Things seem normal now. I can't make it fail by wiggling the battery.

I was wondering if vibration from the mount plus slight play in the battery position caused
fatigue failure. I may try a wedge as you suggest. Not sure whether to try and return
the original battery, or take it apart and see what exactly happened.
If the clips are not broken, but just not making contact with the connection pins properly,
it looks like it would be possible to squeeze them gently with needle-nose tweezers. Being gold-plated, there should be no corrosion problem or "bad spots".