Concerning this case, SmartBear support found a solution, here it is:
I've checked your project suite and I think I know what happens. According to the screenshot associated with the error message, there are multiple dropdown controls on the same screen of your application. As far as I know the DX controls implementation, this means that each of the controls has its own dropdown window associated with it. Therefore, the Aliases.Horizon.PopupLookUpEditForm object may refer to any of those dropdown windows, not necessarily the only one which is currently displayed on your screen. I believe the "The window is invisible and thus cannot be activated" error occurs because the recognition criteria of the Aliases.Horizon.PopupLookUpEditForm object are not unique and therefore TestComplete obtains an invisible dropdown window, not the one you need, during test playback.
This problem should be easily resolved if you add the Visible=true and/or VisibleOnScreen=true criterion to the list of properties used to identify the Aliases.Horizon.PopupLookUpEditForm object in your Name Mapping scheme (see the "Adding and Removing Identification Properties" (http://smartbear.com/viewarticle/75986/) help topic for more information). This way, the Aliases.Horizon.PopupLookUpEditForm alias will always refer to the dropdown window which is currently displayed on your screen. Does this help?
Regards,
Aleksey Kolosov
SmartBear Customer Care