Add me to the list of people who have had this problem for over a month. Typically, every few months, a couple of the devices will ask me to log into iTunes/Facetime/Messages again. I do, and then that's it. That enough has been annoying. Starting a month-ish ago, about once a week, one (any one) of my several devices would ask for the login to several apps again, and after logging in, it would say my account is locked. Then I would have to log in on my main phone again, three laptops, and two ipads to set up the message forwarding again. MAJOR pain because if any message comes in when forwarding isn't set up again, that device will never get the message - this has been a HUGE problem on Apple's end that the iMessage cannot be re-synced.
About a week+ ago, it went from once a week to every other day that I would get locked out and have to go through this mess. A couple of days ago, I finally opened a ticket. I got bumped up to an advanced tech who had to escalate the ticket to the engineers. He did tell me they had found a an authentication bug they were working on that was a little different from this, but really, I think it has to all be related.
One work -around I may have just figured out. This time, one of the ipads said I needed to log into iTunes. I checked my phone, and iMessage was still forwarding correctly, so I wasn't locked out yet. I logged into my AppleID in the computer browser, and I got in normally (security questions) - no unlocking needed. Once I did that, it seems like everything was ok again. I will have to try this again next time I get a pop up to see if it is a real band-aid.
Devices logged in: 2 phones, 2 ipad minis, 3 laptops, 1-3 Apple TVs, 2 Rokus. Only five devices have iMessage linked to the main phone.