I too think the PSU could be the problem, a PSU can definitely fail gradually especially a cheapo one like you have. Cheap PSU's usually have low quality capacitors (the electrical components responsible for filtering and stabilizing the output power) and these low quality capacitors are prone to gradual failure. If you want, take your PSU out and leave it sit for a while to discharge, then take it apart and remove the cover. Don't touch any components on the board but look for the capacitors (round cylinder looking parts usually with a metallic circle on top). If there is orange colored stuff leaking out of the tops of the capacitors or the tops look like they have bulged out the capacitors are failing. As capacitors get worse they can't handle as much current (amps) and the power output is no longer smooth (it can have power spikes), components do not like unstable power and can have errors, especially graphics cards which use a ton of power.
We can't say 100% what the issue is, but a cheap power supply is often the cause of problems. Buy a good 550-650W PSU from a quality brand (Corsair, Antec, etc, I think Rosewill's more expensive PSU's are good but they do make some cheap ones that you should avoid) and see if that solves your problem. If the card isn't overheating or overclocked I doubt the card itself is faulty.