I got my unit back from dell yesterday. According to their paperwork, they replaced the battery and the battery connections (I've not seen inside the unit, so i don't know entirely what that means).
But after speaking to a care representative, there may be an issue with some units in that the battery is improperly installed, and when uit is moved suddenly, it loses the connection between the battery and the unit (it sort of "shifts" inside the case).
I can't speak to the statement's acuracy. Regardless, I tested it extensively last night for quite a bit on battery power and I had no sudden shutdowns. So here's HOPING that did the trick.
EDIT: Day 2 and still no sudden shutdown. So far, so good. Used it extensively last night.