Exact same problem here on my iPad 2 Air.
I say, it started in Nov or December when the last update was installed.
I'm on 12.4.9 now and get nagged once or twice a day ever since.
What I tried:
- change the password
- reboot device
- check for updates
- verify that iTunes has my credentials (another thread suggested, iTunes might cause the popup)
The super weird part is, that when that popup comes, it will ALWAYS lock my account, even when I 100% enter the correct password.
And I then have to complete the unlock procedure (with the very same password) to unlock.
Never had that problem before. So I say it's a bug in the 12.4.9 iOS.
It's super annoying and I wonder why Apple has not commented on this by now.