The time vortex and the Doctor's constant brush with death.
The Doctor travels in the TARDIS through time and space via the time vortex. The vortex is a set of pathways through time and space.
I know, duh.
But I think the vortex represents brushing with death constantly. Space is deep, dark, and lonely. The deepest parts of space are almost like death continuously coming after the Doctor. Maybe that's why he is always on the run, traveling, helping. Yes, part of that is because it was his adapted name due to his constant desire to help and heal. However, I think he needs to run because he travels through the time vortex. Perhaps traveling through the vortex changes you internally. Well, we know it does. In fact, it was looking into the time vortex that created the race of time lords.
Perhaps as death chases the Doctor through his long life, the Doctor must always continue to zoom past the grim reaper, in the tardis, in the other direction. Perhaps it's simply because death can't catch the Doctor, that the Doctor lives so long. Maybe even a higher power provides him with the ability to regenerate. Maybe the Doctor, and the entire race of time lords, are some sort of miracle.
Maybe sometimes, just sometimes, Death is able to clip the Doctor as they cross paths. Perhaps it is this that brought the Doctor and Rose back to Satellite 5 in the Bad Wolf episode. Actually, a few times the Doctor is either running from predators (the Family of Blood) or getting swept into dangerous situations (psychic container anyone?). These seem random at times. Perhaps it's death nudging the Doctor just a little bit, before he loses him again.