My first thought is the power management is tripping. Control Panel>Power Options and dig around.
Second is to use BatteryInfoView from Nirsoft in logging mode to see exactly what state the battery is in when it shuts off (set logging to like every 15 seconds and see what the last record (and trends from earlier ones) looks like).
Third is that something shut it down and there should be a record in Control Panel>Administrative Tools>Event Viewer.