If we can prolong life endlessly, it would not be desirable.
An immortal life would have satisfied all its desires and achieved its goals. There is nothing left to do, but boredom.
Bernard Williams in "The Makropulos Case: Reflections on the Tedium of Immortality" in Problems of the Self, Cambridge: Cambridge University Press, 1973, pp.82-100, argued that immortal individuals would be utterly bored with unchanging desires.
Read Bernard Williams article "The Makropulos Case"
A Reply to Bernard Williams argument.