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I charge my nano until it’s fully charged but it runs out of battery about 2 hours later.
It does sound like your battery is ready to be replaced. Follow this guide to show you how to get to the battery. It is a bit of a PITA due to the size of the Nano. Of course, before you take it apart, you could also give this a try. the battery is available at places like this. I hope this helps, good luck.
Maybe Its cause since it is so tiny that the battery should be tiny to so that means a little bit of battery