Hi Uncanny Ken,
Sorry for the delay, I was dealing with a home plumbing crisis. First, I'm sorry but I have to ask this question: Are you clicking on that link in the Menu Editor, or on the front end of your website?
Also, would you be able to take a screenshot of one of your submenus in the menu editor, and a screenshot of the menu you've embedded that submenu on (also in the menu editor) and provide links to those screenshots?
What type of menu items do you have added to the submenu? Pages, Categories, etc.?
Finally, have you enable WP_DEBUG and looked for errors or warnings on the front end of your website?