It does happen to me when the cellular signal is low/lost. I think it is because even when you have music downloaded for offline play, the Music app still has to confirm that you have an active Apple Music subscription active.
I was doing some "testing" during a drive upstate NY (2.5 hours each way) when I only played from the iPhone with the "show only offline" music selected. (A playlist of 200 songs and several single albums also added.) When I went into Settings/Cellular it appears that I had used about 15MB during the total of 5 hours of driving. Don't think that that is enough to actually stream 5 hours of music, but certainly within reason to think the Music app is checking as I went along that I have an active subscription.
What I don't understand is why can't the app - if you are playing offline music - just check when you start playing music, instead of what looks like each time a song starts.