"Now, this new patch has done away with the hover over menu function and even though we use a positive click to trigger the dropdown menu, TestComplete is returning an error 'object not found' even though the dropdown is appearing."
So the test runs to the point where you click the menu item which triggers the dropdown. This all still works and still happens correctly yes?
So your issue is that the DropDown, although present, is no longer recognised?
Which would suggest that it's just a mapping problem. So either the structure has changed, and your dropdown is not present in the same place in the DOM as it was before, or they have changed something in the properties which has affected one of the properties you use to identify it, or one of it's parent objects.
Have you tried simply re-mapping the object?