I have a mid 2009 Macbook pro 15" that runs fine when plugged in, but not on the battery. When unplugged it will run for a period of time on a fully charged battery then shut down (immediately, not hibernating). If the machine is stressed on battery it will shut down immediately. I've replaced the battery, no change. The battery seems to be charging properly.
All this makes me suspect a voltage regulator, a loose connection on the board interface to the battery, or an intermittent short. Does anyone have any experience with this kind of problem?