have you tested each individually? also, make sure the power connectors are properly clicked in and each cards are fully in the lane. If you are using an ivy bridge processor it may be using PCI-E 3.0 in one lane and not in another which would disable crossfire. can you list system specs?
I have tested both individually they both work just fine by themselves.
corsair 16G DDR3 1333
sapphire radeon hd 7970 diamond radeon hd 7970