When a computer freezes after running X-Plane for awhile, the problem is almost always heat related. When the system is running X-Plane, the video card and processor get very hot because they are running at 100% utilization. This causes the temperature to rise inside the case. To eliminate heat as an issue, remove the computer’s cover and aim a fan into the case. Run X-Plane for a while and see if the problem goes away. If it does, then you need to add some additional cooling.
Note: This assumes that the system has enough RAM. Running out of RAM will cause crashes as well. At least 1 GB of RAM should be used for current versions of X-Plane (more on Windows Vista and Windows 7). This also assumes that the computer is not overclocked.