Sci Fi short story about a fight and a decades-long chase through space

I'm looking for a short story I read long ago. I thought it was Larry Niven but I can't find it. All I remember is that there were two men who got in a fight. One takes off and the other chases in their spaceships.

They chase each other for decades (centuries?) until they can't remember what they were fighting about. Their autodoc (or equiv) keeps them healthy along the way with the ships basically going the same speed and never catching each other.