Using the 'Save As...' command results in duplicate names in the Stored Displays list. Deleting one of the duplicate stored displays deletes the original.
This issue is likely related to the following bug resolved in ArcFM 10.1.
Issue Id: MM43526: Using 'Save As...' to save stored display with same name, results in list of duplicate stored displays on tab.
Specify a different name for existing stored displays when using the 'Save As...' command.