I had the same problem. The 27" Cinema Display would turn off automatically after 5-10 minutes. On turning the power off and then on again, it would come back on - if not at the first try, then at least on the second or third attempt. Additionally, sometimes the display brightness would fall significantly sometime after the display had come back on. But if the display brightness did fall, the monitor would stay on thereafter and work without any problem for the whole session! Now every time I sat in front of the computer I started wishing that the display brightness would automatically fall. This went on for a year, and out of frustration I was almost on the verge of sending it back to Apple for recycling.
Then only a couple of days ago I found that if I turned off the auto-brightness setting and manually decreased the brightness to about 3/4th the full value, then the monitor would stay on and never turn off automatically! It has only been a couple of days, but I haven't had the display turn off automatically since. Maybe this can solve the problem for some - if of course working with the reduced brightness is an option.
It seems that while the problems people in the forum are reporting are very similar, they are not exactly the same. For example, in my case reconnecting the mini-display port won't have any effect, and I haven't seen anyone else in the forum reporting an automatic drop in brightness. So don't get your hopes up, but do try manually setting the brightness to a lower value once and then see if the problem persists. I have visited this thread many times in the last year looking for hope and help. I hope this trick help you. Thanks!