I had disabled the Content Indexing for several mailbox databases during a cross-forest Exchange migration, and needed to rebuild the indexes. A quick google search resulted in this solution, and I did what was described in that article:
The indexes were still not rebuilt, so I had to do some digging.
A quick browse through the Event Log gave me the answer:
When a mailbox database has an activation preference, and is not mounted on the preferred server, the indexing will be listed with status “FailedAndSuspended”. Exchange will automagically move the active database to the preferred server, if all is well in your Exchange environment.
When the database is on its preferred server, the indexing service will start crawling / indexing.