I'm guessing that if you're using Sleepless to keep it awake, and you're keeping it in some sort of bag, it's overheating to the point that it is shutting off to protect itself from permanent damage. Most PowerBooks are intended to be run closed, but on a desktop and connected to peripherals. It gets ventilation on the desk, not in a bag.
Rather than destroying a $1000+ piece of equipment, it may be better to spend about a hundred bucks on an iPod shuffle.