I don't think that's true...
The neurons do have some form of regeneration, they are still of quite a limited source. They can't regenerate and heal themselves, so if a brain cell dies, it dies, and there's very little you can do to replace it. I guess if you supplied the brain cell a consistent supply of energy in a completely sterile environment, you would live forever, but a body couldn't really do that for you, even a cybernetic body with motor functions could have problems with the brain, perhaps collision or just general movement destroys the brain partially, for a long time, eventually causing significant loss.