Have you tried other, similarly demanding DirectX 11 games recently?
Check exhaust fans, etc, to make sure they are clean and working properly. The playtime decreasing with the time the computer has been running is consistent with heat issues. If you quit and restart immediately, do you get another X minutes of playtime, or is it shorter?
Try lowering the graphics settings and resolution, and switching to Windowed or Fake Fullscreen display mode, to see if that will make a difference.
