My telepathic computer solving technique isn't quite perfected yet, so before you jump to the conclusion it's the monitor, here's a few simple things you can check to isolate the exact problem:
1) as newbie as it sounds, have you checked Windows power management on the monitor (start, control panel, power options)
2) Pull all the cables out and plug them in again. (again, sounds newbie but every 1/100000th problem the cables are the problem)
3) Go into the BIOS screen and let it sit there. does the monitor still turn off? (if it does, it's not Windows or another software issue)
4) At the time the monitor goes off, does it feel unusually hot in any places?
5) Have you tried the monitor on another computer? It could be your video card that's at fault.
If it occurs even on another computer, you've isolated that indeed it's the monitor.
Some other questions:
Have you timed exactly how long before it goes off?
Does it repeat this time exactly or is it totally random?
Does the time before going offline seem to be quickening?
Does using a cooling fan blowing on the back of the monitor effect the time before shutting it down?
Do you believe Elvis is still alive?
If anything, if you decide to get it repaired, showing the technician all the tests you've done will show you're not a newbie and he can't rip you off.