Is it a specific game/program that causes it to crash, or does it crash the moment you go into crossfire? How and what are you doing when it crashes?
Also, have you tried both cards independently in both PCIe slots? Maybe it's one of the PCIe slots that's the problem.
And lastly, what is the PSU you are running? A bad or low powered PSU can't handle two 6970's.
Oh yeah, one more thing, do you have MSI afterburner loaded at start up? If MSI afterburner isn't configured for your new setup, it can cause lock ups. Even when it is, the last version I used caused problems at boot up and often locked me up.