Thanks for reaching out about this in the Community!
We'd recommend you run a clean reinstall of the app, following the steps in this Spotify Answer. After that make sure that the Repeat button is not green and doesn't have a small "1" above it. This would indicate that a song is set to repeat.
Another thing you can try is to enable Auto Play from Settings.
If that doesn't help, let us know if this is happening with any playlist you've downloaded for offline listening.
Keep us posted 🙂
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