Active Directory sync profile doesn't remove user from ServiceDesk groups

Our sync profile is configured to synchronize users as well as groups between AD and ServiceDesk.  When the sync profile runs, users who have been deleted from AD are deactivated in ServiceDesk, however, the associated groups don't get updated, i.e. it doesn't remove a user from any ServiceDesk groups even though they've been removed from those respective groups in AD.  Then our automation rules try to send messages to the nonexistant users.  Is the sync process supposed to work this way?  Am I missing a configuration step?