See here for other people who have experienced the same problem and who are annoyed at Apple's lack of response. In any case, my Thunderbolt display now begins to flicker at random times and then turns completely black. So far, the only way I have found to revive it is to unplug the power cord of the monitor, wait a few minutes, and then plug it in again. That is, of course, no way to work (or play).
Sorry to bother you all with my problem, but it might be a warning.
In any case, I hope that my 1000th post will be about something else. (I am now at 907.)