Have there been any experiments that have kept neurons alive (stationary), without preserving methods such as freezing? If yes, then how long were the cells kept alive for?
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'.