game turns off after a couple of minutes

Robert, great little machine you got there. The Vectrex is really more related to a TV than a modern game console. My first suggestion would be to check on the the capacitors on your power supply. I would think that they are getting hot and ultimately will lead to your system shutting down. I currently am working on trying to resurrect mine and can tell you that there is not heatsink on the caps, and plenty of caps on there. Check for bulging and leaking capacitors. Watch for a dark oily discoloration on the logic board, which would indicate a leaky capacitor. Avoid skin contact with that substance. You can download the service manual for the Vectrex right here. Hope this helps to get you started. Good Luck.