Can the VGA or DVI cable be replaced? might be worth trying a different video cable as there could be damage causing a short. Also the monitor could be over heating I've seen that in some places with animals etc that the vents get so clogged the heat cant get out.
Really with out more information all i can do is take shots in the dark here. But trying a different video cable if you can would be a worth while test and also try plugging it directly into a wall socket i know its not recommended but say its on a power bar and its at the end of the bar it may not be getting enough power or there could be a problem with the bar itself.