Using a 850 watt with 2 12 volt rails.
If your PS is at least decent, it cannot be the cause. I use an extremely good 850W PS (Corsair TX 850V2, actually made by Seasonic) for a system with two overclocked 7970, 24/7. I can also overclock my i5 2500K to 4.6GHz@1,46V (about 170W itself alone)... plenty of fans... and there's room for more stuff.
I'm mining with diablo/gui and it still crashes. My OS does crash first, but I did reinstall drivers with driversweeper and it still does it. What's funny is that the card works fine playing games for 8+ hours straight.
Well I don't use Windows, but... tried with Furmark? IIRC, in Windows nothing is as heavy as Furmark. If Furmark is stable, mining must
be stable: if it's not, IMHO your problem is surely software related.