iCloud Music Library and external HDD here's a issue – since I moved my iTunes Library to external HDD, every time I launch iTunes it asks Apple ID password.



When I enter the login/password – all works almost perfectly after that, e.g. I can use iTunes Store, download my recent purchases. 

“Almost” because except iCloud Music Library:



And the same issue repeats if I close and re-open iTunes, it asks Apple ID password again. Any ideas how to solve this problem?
I just had the same problem after moving my iTunes library to my home NAS. Deauthorising and then reauthorising worked for me.