The card is not giving information to the monitor anymore. This is probably happening because the card itself is shutting off the data flow. The question is: why is the card stopping the flow? The monitor is working fine; it's going into standby once there isn't anything to display.
My theory, and the theory of most of the posters here is that the card is shutting down due to insufficient power flow. The voltage to the card must drop below the needed levels and it then shuts down. Not rocket science, just logic. The overheating component theory is still valid, too, but much more rare.
We need to know the wattage of the power supply to see if that's the problem. Many psu's say 500W or something, but that's only their peak performance, not intended for more than a couple of minutes. I think his psu can't support the card running.
The game continues to run because only the graphics card has shut down, not the computer. Everything else is running fine, it's just the gc that isn't getting the power it needs to output all that info to the monitor.