Neurons will reproduce in vitro, but in the CNS the surrounding cells release inhibitors that tell them not to, and no stimulants to tell them to. So there's very little reproduction.

The brain would die at the end of its lifetime whether it was in a biological body or robotic body. The reactivity of oxygen is what causes death by old age. The very nutrient that keeps us going is what eventually makes our cells pack in. Hence it doesn't matter what kind of body supplies oxygen (and other nutrients) to the brain it would still die anyway.

 

Yep. Sadly the very thing we need for life actually kills us - mmm philosophical...