My K750i used to do this. It was the "springyness" of the battery terminals going down slightly, meaning that on any slight knock the electrical connection would break and the phone would instantly shut off.
Easily solved by bending a small piece of ~160gsm card around the bottom end of the battery. The idea is to force the battery up a bit harder onto the terminals.
I don't know if that's the problem, but if it is, that should solve it. Worth a shot in any case
Jon