I don't have an Edge 500, but my 705 has several different modes for determining distance and speed. It's possible to tell the device to use only the speed sensor, combined with a wheel size that you enter manually. If the wheel size is incorrect, you'll see errors in both speed and distance traveled. In general, you should probably have the unit use GPS to determine distance and speed or you should make sure that the wheel size is set appropriately.
The Edge 705 also allows you to set the speed at which the unit considers you stopped. If that number is set too high, it might account for the auto-pausing.
My Edge 705 was also a bit flakey when I initially installed it. Turned out that the battery in the speed/cadence sensor needed to be replaced. If you press the test button on the speed/cadence sensor on don't see a consistent, visible light then the battery might need replacing.