What causes Nintendo Super NES game console to turn off when playing?

SOURCE: Super NES is Driving Me Nuts!

Turning your console on and off *can* erase save game data. This is in the users manual. Intermittent operation on older electronics indicates an internal connection problem somewhere. See if Nintendo can direct you to a fix-it shop, as they no longer service SNES consoles. Failing that, ask local video game stores and rental stores where a good fix-it shop might be.

SOURCE: Original nintendo games on LCD tv

NES games on the Wii's virtual console can sometimes have display issues because the NES only supported 240 lines of resolution, which is stretched over a standard TV with 480 lines.
Making the jump to HD,on a TV that can do up to 1080 lines, there's rare occasions that more issues could come up.
I have never had any issues with Virtual console games on my HDTV, but there is a solution for finicky TVs.
Plug a nunchuck into your Wiimote before starting your NES game. When the game starts, click on Operations Manual. When the Operations screen comes up, press the Z button on the nunchuck, and the a button, and 2 button on the Wiimote all together. You will hear a sound indicating you did this right. The system will auto ajust the game to your TV, so when you exit the operations screen, the game will display correctly.

SOURCE: nes flashing black and white and making a horrible sound

a 'front load' nes ALWAYS does this, even if the connector pins inside the console are new. the cartriges on a Front Load nes rarely completely seat, as Nintendo redesigned the Famicom very poorly for the US market. try this 1. put the cart in as usual, but hold it all the way down 2. slip an unwanted/extra cart in on top of the metal hoop above the cart your using. this gives a better contact for the cart. try cleaning the cartrige pins as well. some won't read right if there's ANYTHING on the pins.

SOURCE: Video Problems with Super Nintendo

Try replacing your video cord. Sometimes they are just "patially bad" meaning they can read something but not enough to do anything.

What did you use to clean the games?

SOURCE: Nintendo NES Repair

Hi sounds like your console has a weak connector pin and is lsing contact with your game. I fixed mine buy purchasing a new connector pin from www.gameoz.com.au and it included step by step instructions with photos and a few tips on how to clean NES cartridge games as their is no use in installing a new 72 pin connector if you dont properly clean the NES games because installing dirty games into a new connector pin will result in console blinking flashing again.