im having the same issue with my laptop (ROG g73jh, i7 1.66ghz 8gb RAM, Mobility Radeon 5870)
Its strange because if i leave the laptop for half a day, it will run for countless hours without glitchin... then suddenly the screen starts flickering.. then a while later it just makes a noise and freezes into a black/green striped screen..
1) check driver, OK its the latest driver from ATI (version 10.9)
2) graphic card overheating, COULD BE but let me remind you that the model i have has a decent airsupply. Plus i dont leave it on the bed or play in the sun.
3) Laptop busted, NOT LIKELY runs Settlers 7, Civilization 5, WoW at highest graphics (sry i dont have crysis or Flight Sim X) and they all run as they are supposed to.
For a few days after i received the game, it ran perfectly on highest settings. Then this happend...
I have an Alienware desktop juiced up but with only a GTX 260 1gb, which has no problems whatsoever (but the graphics arent as good as on the ROG)
maybe this game isnt a WoW-killer, but it sure kills hardware!