Is there any rhyme or reason as to whether or not a horse will run after their rider falls?

I think it s mainly personality, but a horse who doesn't do it can be trained to stop. I never taught my horse this and he always stops. One time he spooked and I was bareback and fell, and he still stopped even though he was scared. Another time we both fell on the trail, and he just laid there until I stood up and then he got up. I've fallen off of him a couple other times and he always stops.