The good news is that its not the game, resource sucking hog that it is.
The bad news, is that if its causing your video to stop displaying, depending on the error (if one is visible), its something with your system, regardless of whether or not it happens just with GW2.
Unfortunately, even with knowing specific information (which you didn't give) its a complete pain to troubleshoot, so I'm not going to bother taking wild shots in the dark beyond the following, because there are hundreds of possible variables, from hardware failure, viruses, improper file security permissions to driver issues, overclocking or file corruption... that this could easily become a 50 page thread just trying everything.
GW2 is almost like a benchmark testing program, its going to push any computer system to its limits, more so than most other games and programs, so it doesn't surprise me that issues with something that might be failing will appear to only affect GW2, especially if its hardware.
It could even be something as simple as your Power Supply beginning to fail, symptoms are similar to what you describe. You can find more information via Google or Bing searches. If you're running nVidia, make sure you upgrade to the current drivers, first, though. There is a rendering issue with previous drivers that can sometimes cause a driver crash at the kernel level.
That's all I have, so good luck.