Well, medically we are yet to determine the cap of the brain cells/ neirons. Other than the inherent capacity to survive, survival of neurons and supporting cells would also depend on a few factors such as nutritional supply, trauma by external agents etc. While most cells in the body are pre-programmed to die, medically termed as apoptosis; neurons usually exhibit a longer lifespan unless the external environment is affected. While on one hand a few cells such as cancer cells become ‘immortal’ by bypassing apoptosis, most cells do not survive beyond a few years; these just being areas of current medical research.
Hope this information is helpful.