Could be the circuit board that connects the battery to the laptop. Could be the battery - did you buy a new one or one off eBay? Could be the motherboard.
I'm assuming you're not running the battery down all the way, which would eventually cause the laptop to shut down completely.
If you're adventurous enough, you could crack open your iBook and see if the cable that connects the battery charging board to the motherboard is crimped or damaged.