I would play it so much back in the day that the battery would die pretty fast. I would always keep my PSP when I'm not playing plugged in so it's always charging. It's the best way to do that because if you don't and you forgot how much battery life you have left then you won't have much time playing the PSP before it dies. Then you would need to charge it up so might as well always keep it plugged in when your not playing it!
It depends on how much I'm playing at it at the moment. Since I tend to go through phases. If I'm using it regularily though I try to charge it daily or at least before I know I'm going to be using it.
I used to have the same problem with the charging aspect of it, and my battery would be dead mid-game for me. Now, I pretty much charge it whenever possible, especially when I'm taking breaks in the middle of a game to get snacks, go to the bathroom, etc. I find it's more convenient that way rather that sitting down and waiting for it to be charged enough to play. I don't think I've had a problem with low battery since.
I don't have a sony handheld anymore but I used to have one. I had the PSP. I didn't use it a whole lot as there just weren't many of the games or genre of games I enjoy the most available for it. Mine had decent battery life when I would play on it though, I could play for hours then turn it off and turn it back on and play for at the least another hour or two before needing to charge it again.
Honestly, I just charge mine whenever it needs to be charged. The battery gets low, I charge it. Sometimes I leave it on the charger when I'm not using it, too. But I wouldn't say I charge it a specific amount of time or specific time I choose to charge it. I'm like DearSweetAru here; I have on and off phases with mine, so it depends on how much I'm using it at that moment. Right now I'm not playing it at all so its just sitting in my drawer, but next time I get into a game on there again I'll probably be charging it every night or after every gaming session.