I also have 2x XFX R7990's and had this problem. Turns out that my Lepa G1600 PS has multiple 12V rails, and the cards are pulling more than the individual rails can handle. If I had a single 12V rail, this probably wouldn't happen in the first place.
By the way, I put a power meter on the AC line into the rig and found that a single R7990 card is pulling over 600W when mining over 1.2MH/s. Assuminng that both PCIE power connectors are evenly balanced, then 300W=12V*25A. So, each card needs approx 50A @ 12V.
Im looking for a new PS now, with the 1600W range, but using either 1 or 2 12V rails rather than the 6 rails that my G1600 has now.
Another option to consider is a stand-alone 12V@100A PS to power the PCIE power connectors on the cards, then using a 350W PS for the mobo. Still thinking about this option, haven't tried it yet. I think if I tie the grounds together it should work...
Thoughts?
Oh, forgot to mention that I have both cards running now, but at reduced MH/s so they don't pull as much power. Seems to be working, but not an ideal solution. Only getting about 800 KH/s currently per card...