Yes, after a while the battery does die down. It depends how often you use it during the day. If for example, you use it for a good ammount of time during the day and you keep skipping songs, forwarding... or whatever causes the ipod light to go on, the battery life goes down a lot. If however you don't do this to often, I believe that the battery life can last for several hours when it's fully charge (maybe about 5 hours).
I hope this helps

when i first got the ipod i made sure that i fully charged it before i even used it. I have had friends that only charged it half way or so and then after that it would never fully charge. Also you should watch out for alot of skipping or picking other songs. Its best to leave it on random for the max battery life. You should on average get like 5 hrs of play

You can also turn the brightness down a bit, don't play the games if you need the power to last, and like imaginepower said, watch out for skipping songs, that (for some reason) eats up battery life.

The battery dies down after a while as it is a lithium ion battery. It can be replaced by hand or by Apple for a somewhat hefty fee. I'd suggest replacing it by hand or asking someone good with small tools to replace it. Otherwise, just turn the brightness down and listen to music instead of playing games or looking at photos. The iPod battery lasts longest playing music uninterrupted.

I get around 15 hours or so before I need to recharge

Hmm that seems low. Maybe you should have it looked at. I usually get a good 10 hours in. Also check your idle screen time.

I think enough people answered. Do you still need help?