I also have the same problem with my notebook. MS Windows 8.1 and display port <=> HDMI connector. I didn't try to resolve it by disconnecting the external monitor because this is not what I want to. It stopped working since I started using version 13 of TeamViewer.
Show them that they're losing customers by chosing not to prioritize a serious bug like this. For my part, they've lost a customer with 120-130 users.
What have you moved to Frank? I have about 10 users. Teamviewer has been very helpful but right now is no use.
How do we make them prioritize this?
Try updating to the latest version - I think they have fixed it now. It worked for me anyway so I am happy.
Sadly, not for me with recent NVidia drivers.