If an artificial life support system can keep the brain supplied with the necessary fluids and oxygen, then the brain could continue to live within the artificial carrier for vast amounts of time as nerve cells age slowly compared to other organs.
The brain could be supported within the artificial carrier with hormonal-biochemical and energetic substrates that maintain the organic tissue.
Advances in nanotechnology and medicine would greatly improve the longevity of the organic tissue, meaning that biological immortality is possible.