Scenario: After performing maintenance and rebooting a Exchange 2013 mailbox server, the Database Copy Status may show healthy, but the Content Index State may show failed. (you can check this by running Get-MailboxDatabaseCopyStatus <dbname> )
Resolution: Give it some time. About 1/4th of our databases Content Index was failed after server reboots. It took about 20 minutes and the Content Index automatically became healthy again.
If you have given it time and it has not became healthy, you can rebuild the Content Index by using the following command: update-mailboxdatabasecopy <dbname><servername> -CatalogOnly. The database does not need to be dismounted in order for this to run and this is a relatively quick process.