Turn the game off when you're not going to use it. The monitor will last longer.
Without knowing what game you have, whether it's a dedicated or conversion cabinet, and the make/model of the monitor I can only give generalizations as to your problem. It could be a 'hum bar' rolling thru the picture. Make sure all frame grounds are secure and connected to the monitor metal frame, isolation transformer frame, power supply frame ground, line filter frame, and green power cord ground wire. Be sure the ground prong has NOT been chopped off the power plug. Check you wall outlet for a good ground. Lastly is make sure a capkit hasbeen installed recently on your monitor.