Phone freezes / shuts off when not plugged in
So here's the issue I'm having:
the phone randomly (or seemingly randomly) freezes shuts off.
The only action that will bring the phone back is a hard reset (i.e. lock+home key held down for 10+ seconds).
The freezes / shut downs do NOT happen when the phone is connected to a charger - either wall or USB.
How do I fix this?
UPDATE: To clarify, I tried factory reset, restoring the phone from iTunes, etc. Nothing has worked so far.