The Apple ID you entered has been disabled for security reasons.

Since Friday (when I replaced iPad 2 with new iPad), I have been getting this error message at least once a day (sometimes twice):

The Apple ID you entered has been disabled for security reasons. Touch "Reset" to change the password.

Click to expand...

The first time I got the error, I changed the password and updated password in every devices and apps that I can think of (Settings, iBooks, Game Center, iTunes, App Store in iPhone and iPad; System Preferences, iTunes, and Mac App Store on MacBook Pro; and even Time Capsule).

But the error persists and pops up every single day, typically when I play a game that uses Game Center. I called Apple support few days ago and they weren't able to narrow down possible cause (they don't think my account is being hacked though).

Help anyone?

It looks like the problem was caused by me not setting old iPad 2's "Automatic Downloads" feature to off. I sold it after selecting "Erase All Contents and Settings", but apparently, that does not remove the iPad 2 from iCloud Automatic Downloads list. The setting was buried in iTunes Store within iTunes for Mac, under Account.

I must have spoke too soon. While my "solution" did work for several days, the problem resurfaced. I think the issue lies entirely in Game Center. It is almost as if it does not like two separate devices (iPad and iPhone) using same ID in quick succession.