First of all, what iOS device are you using, and what version of Spotify is it running?
If you could also let us know:
1) Does this happen to all songs saved in Offline Mode?
2) Roughly how many playlists / albums do you have saved for offline listening?
3) When it stops, does it automatically begin playing the next song in the Queue?
4) Have you been streaming offline for more than 30 days straight, or do you also stream via WiFi in between?
Any further info on from these four questions would also be good to know.
We'd recommend checking for an iOS update, and we'd also suggest a reinstall at this stage. This will mean resyncing your tracks for offline listening, but it should improve your experience in Offline Mode.