I started having this problem today with my Droid X shutting off. Battery was fully charged and I pulled phone out of my pocket and it didn't work. Plugged it into car charger and it came on but once I made a call, it was off again mid-call. Once again, plugged it into charger and it turned on - and I shook it a bit to see if that was the problem and it shut off. I'm going to flash back to stock and see if the current MIUI may be the problem.
Never had any problems with previous builds before and I've been on MIUI since it was first ported to the DX...