Is this a nano with a touch display (6th or 7th gen)? There is a setting called Repeat. If it is set to Repeat One (repeat current song), it will repeat the same song over and over. The Repeat setting button is on the Now Playing screen. The symbol lools like two arrows in a loop. Tap it to change the Repeat setting. The other choices are Repeat All (repeat current list) and Repeat OFF.
If your nano is older, the Repeat setting is on iPod's Settings screen.
That will obviously work, but if you run into this issue again, you don't want to resort to doing that every time.
If your nano has a touch screen, the setting is on the Now Playing screen. You may need to tap the screen (or swipe the screen) to bring up the playback option buttons, such as Repeat, Shuffle, and Genius Playlist.