It seems, because at the moment I cannot think of any other reason why this is happening, it might well be a power issue. But as I say I am a little stumped.
How are you connecting your monitors to the GPU?
Your card can, with out a doubt, handle dual monitors. Can you unplug one of them and run it for a day and see how it behaves, then the other one and swap which connector you use?
The card might well be failing but try my suggestion and post back