Periodically, after doing maintenance on Exchange one or more content indexes will fail in a DAG. I have had this happen as recently as 1/13/2012, while running Exchange 2010 SP1 Update Rollup 5.
The command to check health is Get-MailboxDatabaseCopyStatus
The fix is to restart the MSExchange Search service on the node which has the active database, then run update-mailboxdatabasecopy -catalogonly for the passive database.
