Hello, MrBlueno!
Thank you for using the Apple Support Communities! I understand you are having an issue with your Apple Music continuously asking you to sign in. I am here to help.
If you've recently changed the password for your Apple ID, I suggest ensuring it's been updated with all of Apple services, as described in the following guide:
What to do after you change your Apple ID or password
If you haven't changed your password, let's have you force the Music app to close, restart your iOS device, and test the behavior. See those steps from the following guides:
How to force an app to close on your iPhone, iPad, or iPod touch
&
Restart your iPhone, iPad, or iPod touch
If the issue persists, I suggest signing out of Apple Music, sign back in, and test the behavior. Keep in mind, signing out of Apple Music will remove music downloaded for offline listening. To sign out of Apple Music: you will need to sign out of the iTunes Store by tapping Settings > iTunes & App Store, then tap your Apple ID and select the Sign Out option. You can sign back in through the same setting, or as described in the following guide:
Sign in to the iTunes Store on your iPhone, iPad, iPod touch, Mac, PC, or Apple TV
I hope this helps and you have a great day!
Cheers!