Reboot? It shouldn't do that. It should cause a driver crash and recover, or worst case, freeze. Reboot seems to point to a power supply problem.
Sorry by reboot I chose the wrong word for that. I meant it would go to a black screen and lock up.
Black screen.. I also encounter this problem on specific cards, or at least I'm assuming this as I only have VNC access to some. It usually only happens to me if a card is unstable at a certain frequency, either due to lack of power or excess of heat in combination with high clocks, and has difficulty recovering. Out of 13 cards, 2 of them have some difficulty recovering. One of them causes the screen to freeze and entire rig is unresponsive, but is capable of high clocks at low volts (Diamond 5830 @ 885 core and 0.95v). The other goes to a black screen instead and PC is unresponsive (Sapphire 5830 extreme @ 705 core and 0.95v).
To rule out some sort of power problem, can you see if you can run furmark on all gpus, possible by extending desktop and dragging furmark window the new "monitors"? Use vga dummy plugs if you have to. I found that I get a consistently larger power draw with furmark than with bitcoin mining, and it should rule out mining-specific problems.