Hello Marteto,
Thanks for reaching out to the Apple Support Communities. We understand you are looking for some help with playing music that you have downloaded for offline use. We are happy to help provide some guidance.
Have you had a chance to remove the some of the songs this is happening with and redownload them from Apple Music to see if the issue persists? If not, we would recommend trying that first.
If the issue continues, we would next advise to try disabling the Sync Library option from Settings > Music and re-enabling it to re-sync your Music.
Keep us updated on how it goes. We hope this information helps.
Best Regards.