Re: monitor won't stay on
It is a sign of a failing monitor, unfortunately I think and I also presume that monitors are repaired rarely any more. However, have you checked for a bad cable or connector? Power cord as well as data cable. Try the monitor with another computer to be sure the trouble is in the monitor and not in the computer.
Re: monitor won't stay on
It sounds to me like a low voltage rectifier is going out in the monitor. Get the PSU regulation in the monitor repaired or if it is broken then buy a new one. I also think that your monitor can be serviced, but this may not be cost effective. The labour would be more costly than the parts. If in the case any proprietary parts must be changed, many of the manufactures will not sell replacement parts to support after warranty service.
Re: monitor won't stay on
When you turn it on, and it's running for those 30 seconds, try to quickly turn down the brighness and contrast. This happened to me a couple of times at work with some of the flat screens there. Possibly, try and update the drivers, or flash the onbaord bios on the graphics card. If you want to do that, you have to be VERY sure what bios you flash it with, choosing the wrong bios, can kill your card.