I have an XPS 1530 (running Vista) that keeps randomly powering off (using AC power) in the middle of doing something. It doesn't automatically switch to battery power, it just powers off.
The power settings are correct...not set to power off after a certain amount of time has lapsed.
It's not an overheating problem...the laptop sits on a hard surface when it's powered on. NOTE: I also touch the underside of the laptop to check for excess heat, but it doesn't seem to be overly warm. The fan runs periodically, as it should, to keep things cool.
Since it doesn't seem to be a heat problem, I'm not sure why it randomly powers off.
I don't have a solution - sorry! - but I do have the same problem, though mine is with an M1330 XPS laptop. I had the motherboard and cooling system replaced, but now, often after the screen saver comes on, or when it is set to turn off the monitor, the whole system partially powers down or hibernates, and it cannot be be brought back without completely powering down and re-starting. I recently made sure that the video driver and BIOS are up to date. I, too, would appreciate help!