You guys might have resolved the issue by now, so it would be nice to hear what you have done, even if you have replaced the computer.
My wife has had this problem for a while. The screen would apparently randomly go black and she would reset the computer and lower the brightness. She found that reducing the bright to 5 notches stopped the random "blackouts", of which she complained constantly for being hard to see during the day. Then her hard disk failed, so I took it to the Apple store and had the disk replaced. They also "fixed" the screen issue by replacing some cable (I did not ask, I was happy that they said the issue was fixed). Soon enough the problem returned. Random blackouts, and a constant hard drive read/write noise that was always there but ignored as it was not the biggest issue.
I switched computers with her. Gave her my iMac and took hers, to see if I could experience her problem and read about it. Using the activity monitor (under iMac utilities) I quickly realized that I was putting too much demand on the HD. With only 4GB of installed memory, I quickly required more memory with just a couple of memory intensive applications. I have ordered a memory upgrade that will take the capacity to 12GB and I hope that this will solve the HD problem by reducing the number of read/writes per minute. Would this possibly affect the blackout issue? I think it might.
You might say, "why would you put money into an iMac that has an unresolved blackout issue?" First, let's rule out the level of brightness. The blackouts happen at low brightness as well as high brightness, at least in my case. Are you afraid to trigger the blackout by increasing the brightness and thus having to reset the computer? then the first thing you need to do is to avoid the resetting. Here is how: Whenever you have a blackout, enter this key combination: <option><command><eject> Ironically, this is supposed to turn the screen off. Then wait a second or two and press <any key>. This will light up your screen again. Now you can trouble shoot your screen issue. Turn the brightness up or down at will, to try to reproduce the issue. You will find that you cannot trigger the blackout by simply changing the brightness. However, you may find that it comes back randomly.
Some pleople say that it is an overheating problem and use the SMCFanControl. I am in the process of testing that theory. Here is where the hard drive usage/memory issue might be related to the black outs. If the low memory causes the constant access to the hard drive and this in turn overheats the drive and it is the overheating that cause the screen blackouts, then increasing the Fan RPM's might solve the problem. Better yet, increasing the computer's memory might fix the problem. I will report back!