Your driver/cgminer is bugged... Just try reloading the "saved" card profile, and restart the miner program.
If the problem does not resolve itself, then you have to adjust the settings until you no longer get hardware errors.
I see this a LOT after a short run, or card-cooling, or just an odd profile setting for that card.
One setting will not work for all cards, unless you go "completely safe". Also, running two cards is not the same as running one cards settings. You will have to adjust for the SHARED bandwidth/slots/threads/workload... (Lower intensity, less threads, lower thread values, individual clocks/voltages/fan-control... etc...)
Using any single 16x slot may make it 16x... but using both, may degrade them to 8x each... or only one is 16x, the other turns into 8x... etc... (Less bus-speed/volume)
Could also be that a pin has "dust" on it, thus, no contact... or the card is not completely seated right... (pin touching two contacts, or not touching "enough".)