SQL Server 2012 Maintenance Plan succeeds but does not perform backup

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http://serverfault.com – I have a new SQL Server 2012 AlwaysOn Availability Group on Windows Server 2008 R2 Ent SP1. I'm creating a Maintenance Plan on the Primary Replica which is supposed to do Full (non-copy-only) backups of the only User database. The task is succeeding, the subplan is succeeding, but there is no backup file when it's done. I get the same results when I delete the Maintenance Plan and re-create it from scratch. 'FailPackageOnFailure' and 'FailParentOnFailure' are both set to True on the Subplan and the task. I have also tried enabling 'ignore Replica Priority' in the task, which didn't help. (HowTos)