It almost always happens when my kids are playing games online. A friend said I needed more memory or ram, but he's not all that familiar w/ macs and memory is expensive, so I wanted to get a second opinion.
Check your screen saver and energy setting in the systems preferences. They probably need adjustment.
Your kids might also be inadvertently activating a "hot spot" on the screen. That's a corner of the screen set up to activate the screen saver, or put the machine to sleep.
Memory is not that expensive and sometimes you can find a good deal if you look around. Sounds like you might be overheating the video card, just a guess. If your computer is a little old you might want to check where your computers fans are to see if they are dirty. My comp would overheat due to there being so much dust in it. Compressed air will take care of it, just make sure it's not plugged in when you do it.