The general consensus is that you shouldn't let your battery go below say 15% or so, the best area is 35~40% or around there.
In any case though you should be fine without your battery shitting out on you. I do understand the want/need for your handheld to last as long as possible both shortterm between charges and longterm throughout it's life, but for the PSP it doesn't have the problems that say the DS would run into where you shouldn't play when charging, and shouldn't charge unless red, etc, etc.