If I had to guess, the adapter might be outputting a 1080p signal and your TV only supports 1080i, so instead it downscales to 720 resolution. I've seen that happen before with earlier generation HDTVs.
If that is not the issue, you should collect the information when the problem is happening with the debug tools and post them in your next post. This will help the devs when they look at the issue.
http://www.displaylink.com/support/ticket.php?id=269