Having to repeatedly re-enter my Apple ID password since upgrading to iOS 9.2

Since upgrading 2 days ago to iOS 9.2, I've been prompted several times to enter my Apple ID password. Once I enter it everything in the world of iCloud is fine. But, several hours later, I'll unlock my phone and be asked to enter it once again.

I happened to be at an Apple store last evening and and one of the employees thought it was possible that the iOS was corrupted. Possibly due to an interruption during download over WiFi. He suggested using iTunes to may a backup and then restoring the phone from the backup.

Is anyone else is experiencing this problem?

If I restore from the backup, do I get a "clean" install of the iOS or do I need to "wipe" the phone before doing the restore?

Thanks!