Did you completely charge it and then let it completely drain before charging it the second time?
Sometimes phones/mp3 players and such have batteries that need this done to them so that they hold more "juice" and staying power.
However, if you are playing a lot of games on it, the battery might not last as long. See if you can turn down how long the backlight is supposed to be on as well when you switch songs, and that will help save battery life.
Is he listening to music/playing on it for the majority of the day? If so then that is completely normal. If he isn't using it a lot and it's still loosing a lot of charging power then I would send it back to Apple.
How bright does he have the screen set? If it's at full brightness and he's using it a lot that would drain the battery fairly quickly as well.
I know with 3D games, the battery on mine runs out after about 3 hours. Music lasts much, much longer, and videos are somewhere in between.
What I did was buy the Battery Doctor Pro app. It does the full cycle charge thing once the battery is under 20% ... But the BEST thing is that it gives you a detailed list of things you can do with however much battery life you have left. For instance, if I only have 30% power, it'll tell me I can read a Kindle book for 4 hours, play a game for 30 minutes, listen to music for 2 hours, etc. (Not exactly real stats there, but you get what I'm saying.)