It would be helpful if you provided more details - such as type of monitor, is it enclosed, age possibly... but off hand, I would say you have either an overheating problem, or a power supply failure. Check to make sure you have enough circulation around it - use a fan on it (not too close - magnets you know...) and see if it stays on for a while longer. Try swapping the power supply out if you can do so safely - I don't know your level of experience on this stuff, but it's not for the novice tinkerer. If niether of these work, and it's not under warranty, call around and see what it will cost you to have someone look at it - it may be cheaper to buy a new one - good luck!