I purchased this card last year and it worked OK for about 6 months. Then I started playing WOW. I know it is not that demanding of a game and a single GTX 560ti should easily handle WOW on max settings since I only have a single 18.5 in monitor. About a month after playing wow the card starting getting too hot and i would get blue screens. I bought a $50 ATI (4000 series) card and it handles WOW. I had to lower some of the settings, but it handled the game without getting too hot.
A $50 card handled it better than a $250 card.
This past January I returned it and got a replacement...it took about 40 days. 5 months after getting the replacment card i am having the same issues. This time the card is not getting too hot, but it is freezing up and i am getting blue screens. I replaced it with that same $50 card and it is handling the games I play just fine.
This Gigabyte card is garbage....DONT BUY IT!
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I would look at the rest of your system getting 2 bad cards is very unlikely.
I own a gigabyte GTX 560 Ti myself and it's been a very solid card so far. I don't experience any of the problems your mentioned, and it plays WoW very nicely. It overclocks very easily too.
Sounds like an issue with something other than your GPU.