My problem seems to be unusual as it doesn't do it once, it continuously does it until the game looks like its artifacting.
Whenever i am playing a game such as "Need for Speed: The Run" or "Assassins Creed: Revelations" it will play perfectly fine and then all of a sudden the monitor will turn itself off, then back on and it will continue to repeat this.
CPU: AMD Phenom II X6 1055T (Stock)
Motherboard: Gigabyte MA770T-UD3 Rev. 1.0 (flashed to the latest bios update)
Graphics Card: Gigabyte Radeon HD5750
PSU: 500W (cant remember the brand)
Asus VH203 (20 Inch)
AOC F19 (19 Inch)
The monitors only have VGA ports, so i have an adapter on both to convert them to DVI.
I never had this problem when i was just using the AOC by itself.
Is there any way to determine what is causing the problem?
Well the usual things to suggest first in a situation like this is to eliminate the possible variables to come to a fresh starting point for troubleshooting.
Cleanly remove any and all remnants of the graphics drivers, and reinstall them.
Confirm the issue does or does not happen during single monitor use. Confirm it doesn't happen with the Asus, then confirm it doesn't happen with AOC, or if it does, report the circumstances. Then go back to two monitors connected and confirm it does happen and is repeatable, or if it no longer happens (can hope). Depending on the results of the single monitor tests, it may lead you to testing the monitor's cables, their connections at both ends, different connectors on the monitors, swapping cables, etc. You'll want to rule out all of these possibilities first because they're hardware. Confirming all of that is good to go is the first start.
I wouldn't be surprised however if some Tom's genius pops in and says, "oh do this and yer good to go".