Hello sofdre,
Thanks for using Apple Support Communities. It's my understanding that iTunes repeatedly prompts to sign in, even after the correct credentials are entered. I can see how this could be concerning. I'm happy to help.
If you haven't already, force iTunes to quit and restart your Mac.
How to force an app to quit on your Mac
If the behavior continues, try testing the issue in safe mode. Starting in safe mode allows your Mac to run certain checks, remove caches, and prevent login items from automatically launching. This can isolate possible third party issues. Use the steps and information in the link below for assistance with safe mode:
Use safe mode to isolate issues with your Mac
If the issue persists, test in another user account. This will help determine if the issue is system wide or specific to your user account.
How to test an issue in another user account on your Mac
Let us know the results. Please include specific error messages and any other troubleshooting steps you may have tried.
Have a nice day!