Databases with auto-close enabled are ignored when the "Ignore databases where the state is not online" option is set in a maintenance plan backup task. This applies to all three types of backups.
I'm filing this as a bug given that the state of an auto-close-enabled database is ONLINE in sys.databases.
Note that in the maintenance plan, the View T-SQL window sometimes *does* show these databases in the script; however, when you actually run the job, it never backs them up.
I discovered this problem on 10.0.2531.0 (Enterprise 64-bit on Windows Server 2008 SP2 Enterprise), and reproduced under 11.0.1440 (Denali CTP3 on Windows 7 32-bit).