Chosen Solution

When I plug my nano off, the screen is only effective for a few minutes.when it turns off impossible to make it come back unless pluging it again on AC.

The battery may have to be replaced, remember, no battery lasts forever and this will give all of us a starting point to troubleshoot it Try and source out a battery, and follow this guide, you need to solder, here is your battery. Also, if you are undr warranty, take it to Apple to fix