I have a Win 7 rig with two 5830s. If I mine them at the same time, it works for a random period of time and then reboots. I'm OC'ing with Trixx, heat is not an issue. 600W PSU. One card in a 16x slot one in a 1x with the cablesarus riser cable with the Molex.
I've tried different gui miners to no avail. Upgraded the drivers to 11.6b. Doesn't seem to help.