That is precisely the problem. It is unreasonable to pursue a fleeing felon. Vigilante Justice is not justice. If you go and kill a fleeing felon you are guilty of murder.
Our sacred right to bear arms is predicated on our right to self defense. We do not have the right to go out and shoot people that are no threat to us, we have given that right to our Government.
Does your answer represent the libertarian point of view, conventional legal reality, or what? Just so you know, my thinking, which is implicit in the question posed, is strictly confined to the morality of self defense. I'm open to another point of view. But I don't think we've completely delegated to the government absolute responsibility in the matter of apprehension of criminals who are in the process of conducting a crime. Does hot pursuit automatically a count as a strike against self defense?