I am having this problem as well and went to the Genius Bar and they said it would be tough to figure out without seeing the tv. They told me to try a restart using the Command-R function and it managed to get both screens working on that setting, so I am pretty sure it is a software/setting issue. I am trying to figure out how to restore/reinstall Mountain Lion OSx without losing files to see if that solves it.
FYI, this only occurs when I connect to one of the two tvs in my house. Both are samsung and the one it doesn't work with is only 6 months old. Also, my MBP+r HDMI connection worked for a bit on both TVs and then started to have this issue around 3 weeks ago.
Unfortunately, these posts are not numbered, but the "fix" is my post of September 24, 5:05 pm.
I'll restate it here with some clarifications. But this is not the fix for everyone with MBP-HDMI problems, and as I've suggested previously, you may have to get Apple support.
Go to Finder.
In the root directory (MacBookPro or whatever your HD is called), go to Library, go to Preferences, find com.apple.windowserver.plist and put it into Trash
In your own user directory, go to Library (to see the user Library folder in Finder, click the Go menu in finder and at the same time hold the Option key down, and then you'll see Library). Go to Preferences folder within the Library folder, go to the ByHost directory within the Preferences folder, find com.apple.windowserver.[random numbers and letters].plist, and put that plist file into Trash.
There may be more than one com.apple.windowserver.xxxxxx.plist file in both of these directories, including one that ends in plist.lck--just remove any plist file with "windowserver" in it. You won't cause any harm by removing a plist file.
You do not have to empty the Trash folder, but you can if you want to.
I don't know how to state it any more clearly than that. If it doesn't work, and it may not, especially with non-Retina MBPs, then you have to call Apple support.