The answer is basically that having nerve cells reproduce can do more harm than good. Each nerve cell has a specific place in our nervous system. Its job is all about taking a signal from one specific place to another one. Adding new nerve cells would mess up these very specific connections in a very complex system. So we trade off the ability to repair our nerves in order to avoid messing up connections.
I am sorry to say that the nerve cell fails to replicate because it is very long in size.