Apple ID Password Update Every Day
For the last two weeks I've been asked to enter and/or update my Apple ID password every single day after a power off or restart on both my iPad Air and iPhone 6 both running iOS 9.1. They are completely unusable until I do this, locking me out of EVERYTHING until I type in my password and it verifies it with the server. This problem is not encountered on my MacBook or its versions of iCloud, the App Store, or iTunes.
I have signed out of iCloud, FaceTime, Messages, and the App Store (all use Apple ID), made sure there is nothing downloading in the App Store or iTunes (like a digital booklet), Reset ALL settings, Hard Reset, changed my Apple ID password and re-signed in using Apple ID multiple times. The problem persists.
I have changed the Apple ID itself and repeated the above steps. Same problem.
I've gone so far as to completely wipe both devices, reinstall iOS 9.1, and gone through the hassle of setting everything up from scratch, losing ALL of my data. The problem is still there.
I finally broke down and called Apple Support. After 35 minutes explaining that "Yes, I have signed out and signed back in to iCloud" their tech had no other ideas as Apple System Statusshows that everything is working fine.
How do I fix this?
iPad Air, iOS 9.1, Also effects iPhone 6 (iOS 9.1)