How long can a human neuron live outside the body in a controlled environment?
According to this paper from 2001, they've got the survival time up to about a year on average. The trick is sealing the neuron inside a permeable membrane so you don't actually risk contamination when feeding. This paper lays out experiments that take many weeks to perform, so as far as I can tell the science of keeping neurons alive has advanced to 'as long as I keep feeding them and nothing bad happens'.