Are you sure your little sister/brother/dog doesn't unplug the monitor cable after said period just to piss you off?
Have you checked all connections i.e. power and VGA? Also, this kind of problem is usually due to some connection that has come loose internally, or something that changes due to heat (hence the 5 -10 mins before malfunction). Sounds like something a monitor repair shop could fix. If it's an expensive or not old monitor try getting it fixed, otherwise the cost of fixing it probably isn't worth it.
[ 05-28-2004, 11:33 AM: Message edited by: Vaskez ]