I wasn't aware that some objectivists use Ayn Rand's thought experiments to support an opposition to extended human longevity. The essay linked here refutes that interpretation, but this is only one facet of a much broader set of arguments - found in or arising from adherents of near every philosophy - made to suggest that aging and death gives human life value, or moral or ethical standing. From this perspective the medical control of aging, and the elimination of pain, suffering and death caused by age-related disease, achieved through technologies such as SENS rejuvenation treatments, would somehow make us all worse off. This is one of many reasons why most philosophical positioning, like the theology it evolved from, isn't worth the paper it is printed on, or the time taken to understand its errors. It is self-evidently ridiculous to argue that less age-related disease and more healthy life diminishes us, and I don't see any of the people making that argument rushing to give up the advantages of present day medicine when it comes to treating age-related disease. Hypocrites, the lot of them. Nonetheless, that is is exactly the position regularly deployed against advocates of greater research and development in longevity science. It is both irrational and, to the extent it harms progress, dangerous for all of us.
Some advocates of Ayn Rand's philosophy believe that indefinite life would turn human beings into "immortal, indestructible robots" that, according to Ayn Rand, would have no genuine values. Both of these claims are false. Indefinite life would not turn humans into indestructible robots, nor would an indestructible robot with human abilities lack values or motivation for doing great things. Rand's "immortal robot" argument is found in "The Objectivist Ethics": "To make this point fully clear, try to imagine an immortal, indestructible robot, an entity which moves and acts, but which cannot be affected by anything, which cannot be changed in any respect, which cannot be damaged, injured or destroyed. Such an entity would not be able to have any values; it would have nothing to gain or to lose; it could not regard anything as for or against it, as serving or threatening its welfare, as fulfilling or frustrating its interests. It could have no interests and no goals."
First, at no point in time will human beings become "immortal, indestructible robots". The simple reason for this is that our existence is physical and contingent on certain physical prerequisites being fulfilled. The moment one of these physical prerequisites is lacking, our existence ceases. This will always be the case, even if we no longer have a necessary upper limit on our lifespans. For instance, biomedical advances that would greatly expand human lifespans - allowing periodic reversions to a more youthful biological state and therefore the possibility of an indefinite existence - would not turn humans into indestructible robots. There would still be the need to actively turn back biological processes of decay, and the active choice to pursue such treatments or not. People who live longer by successfully combating senescence could still get run over by a car or experience a plane crash.
Moreover, the need to reject the "immortal robot" argument when discussing indefinite life extension does not stem solely from a desire to achieve philosophical correctness. Rather, we should recognize the potential for actually achieving meaningful, unprecedented longevity increases within our own lifetimes. Thus, it is premature to conclude that death is a certainty for those who are alive today. Medical advances on the horizon could indeed turn many humans into beings who are still potentially vulnerable to death, but no longer subject to any upper limit on their lifespans.
It is therefore ill-advised to pin any ethical justifications for the ultimate value of human life to the current contingent situation, where it just so happens that human lifespans are finite because we have not achieved the level of technological advancement to overcome senescence yet. If such advances are achieved, common interpretations of the "immortal robot" argument and its derivative claims would suggest that life for human beings would transform from an ultimate value to some lesser value or to no value at all. This implication reveals a flaw in arguments that rely on the finitude of life and the inevitability of death. How is it that, by making life longer, healthier, and of higher quality (with less suffering due to the diseases of old age), humans would, in so doing, deprive life of its status as an ultimate value? If life is improved, it does not thereby lose a moral status that it previously possessed.
But suppose that a true immortal, indestructible robot could exist and be identical to human beings in every other respect. Even if death were not a possibility for such a being, it could still pursue and enjoy art, music, inventions, games - any activity that is appealing from the perspective of the senses, the intellect, or the general civilizing project of transforming chaos into order and transforming simpler orders into more complex ones.
The fear of death is not the sole motivator for human actions by far. Indeed, most great human accomplishments are a result of positive, not negative motivations. I concur fully with the goal of a full life, of flourishing, and recognize the existence of numerous positive motivations besides mere survival. For example, the desire to see oneself create something, to witness a product of one's mind become embodied in the physical reality, is a powerful motivation indeed. One can furthermore seek to take aesthetic pleasure from a particular object or activity. This does not require even a thought of death. Creating art and music, undertaking scientific discoveries, envisioning new worlds - actual and fictional - does not rely on having to die in the future. None of these activities even rely on the threat of death. Life is not merely about survival and should be about the pursuit of individual flourishing as well. Survival is a necessary prerequisite, but, once it is achieved, an individual is free to pursue higher-order values, such as self-actualization. The individual would only be further empowered in the quest for flourishing and self-actualization in a hypothetical environment where no threats to survival existed.