Backup failure for a DB part of Always-On Availability group - SQL 2012 Ent Edition
MS discovered that this is an issue with 2012 CU3. We ran into this bug: https://support.microsoft.com/en-us/help/3033492/alwayson-availability-groups-may-be-reported-as-not-synchronizing-afte   

This problem is resolved in SQL 2012 SP4.

In the interim - the solution is a reboot to get the DBs off the bad state.