I think this depends on the generation of the nano. This was true for the two previous nano's I had (the fifth and the third), but the sixth does have a point that it completely shuts down and will reboot when you turn it on. I think it is somewhere between a day or two, I've never really timed it. Just when I haven't used it in more than a day or two it reboots when I turn it on.
My 2nd Gen iPod Touch was left on playing music with the screen turned off. It played for two days before I noticed. I was away at the time. It still had nearly half a battery left! I would say, in my case, it will play a very long time as long as you turn off the screen.😀