Which PB model? It may not be relevant, but interesting anyway.
How old is the battery, or better yet, how many charge cycles do you have on it?
When did you last calibrate the battery?
It sounds like a weak/old battery on a model that does not have a backup battery to maintain the system settings when the main battery is dead or removed for an extended time. As you've guessed, the power supply could be the culprit, if it's not charging the battery properly.