I have a lot of HP EliteBooks in the office here (8540p, 8560p, and 8570p). I have had 3 out of the ~75 here have video card issues where the motherboard had to be replaced. I tried diagnosing by using different video card drivers, monitoring the heat produced by the laptops, cleaning the dust out, and even wiping the machines. The laptops were all under the 3 year warranty so I sent them to our HP Partner and they ran diagnostics and replaced the motherboards for me.
I would suggest try using different drivers provided by the HP website here and see if that fixes the issue. If it doesn't I would try to monitor the amount of heat being produced by the laptop with a tool such as speedfan and possibly clean it out. If all else fails try to RMA.