My TBD started turning itself off about 18 hours ago, after 9 months of problem-free use with my iMac Quad 3.4 i7 16GB 6970M 2GB 1TB. So yesterday afternoon was the first time, and after a reboot it worked for the remaining hour of the day.
This morning it was off, rebooted, nothing. Replugged TB cable, still nothing. Unplugged power for a second, nothing. Unplugged power for 10 seconds, then it worked. 5 minutes later, turned off again. Reset PRAM and SMC on iMac, no help.
All the while, the 2nd display would still appear to be connected in Displays. I clicked gather windows, changed the resolution of the 2nd display in an attempt to trigger it back to life, no luck. Changed it back to native res, then strangely the iMac display never returned from the temporary blue background that it goes through during resolution change. Unplugged the TBD power, iMac restored the primary display. Plugged it back in, nothing. Restarted, nothing (not even showing up in Displays). Replugged the TBD power, nothing.
So now it's totally toasted, it doesn't work at all, not even for a few minutes.
Have tried using it on another iMac and a MacBook Pro, all the same results. Temporarily using a 27" Cinema Display until I get to the local Retail Store as AppleCare Support have said to take it in and get a replacement.
Will update here with the results of the Store tests and how I get on with the replacement TBD.