I have a UltraSharp 1704FPT 17-inch monitor that does the same thing. I have been on the phone with technical support for 2 days with no resolution. Since my computer is still under warranty, if/when I get the problem resolved, I will add to this thread.
I have gotten a response.
That monitor if faulty. It's the same as shown in message: http://forums.us.dell.com/supportforums/board/message?board.id=dim_monitor&message.id=49185#M49185
The support person tried to get me to rebuild the operating system. When I wouldn't go for that, I asked to speak to the supervisor. He requested that I perform one additional test before they would attribute the problem to the monitor -- you might want to try it also.
During boot-up press the F2 button to get into setup. Leave the computer in this mode and see if the monitor still goes to black. Mine did, however the time it took was longer (35 minutes) than during windows operation (five to 10 minutes).
They are sending me a new monitor, however, I guess I'll have to wait 5 months (which is how long I had this one) before I know if the replacement monitor is any good.