Works for a small period, then starts to blink.

Hi there,

I have a problem I've never encountered before with my NES. I will put in a game and for about 15 minutes it'll work great with no graphics problems or blinking. After that time, mid-game the game will start blinking with the starting screen of said game, as if I had pressed reset and the game wasn't fully registering. I've tried three different cartridges, and have cleaned them how I normally would. Is this a pin-connector issue or might it be something else?

Thanks!