My ipod nano connects to my bluetooth headset but it continues to search. My battery died in less than 6 hours when it usually lasts days.

I don't have an Nano but all other iOS devices will always search all of the time that Settings > Bluetooth is open. I think the assumption is that if you have it open you are likely looking for a device to connect to. And by definition, every time you open it to see if it is searching, it will be. The fact that it searches while open doesn't significantly affect the battery on those devices.