Usually it will be simple lockups on the GPU's if you are running on the verge of overloading your PSU. Sometimes the system will randomly reboot. Are you overclocking these GPU's? They will require a good bit more power once you start overclocking them, thats when I started seeing all the problems on my rig. Overclocking with that 5870 just put me right on the edge of stability. My GPU's would lock up and I would be forced to reboot my system and downclock the GPUs.
i only have them oc'd to 875, with mem uc'd to 900. as far as i know, that's all aticonfig will let me do, and i am happy with it, i don't want to push them too hard, the third card temp is 67C as it is (although the others are much lower)