At my customer DAG database indexes get sometimes failed or "failedandsuspended" status.
Solution was: https://support.microsoft.com/en-us/kb/2807668
So, I created the AD group "ContentSubmitters" in "Microsoft Exchange Security Groups" OU with security:
"Network service", "Domain Admins", "Administrators" - Full Control
Propagated through AD DCs, Restarted "Microsoft Exchange Search" and "Microsoft Exchange Search Host Controller" services on all servers in the DAG.
It will take time to settle down, during the time active databases might be moved between servers by the process.