Are there limits on human longevity? Sure. Few people will make it past a hundred years of age in the environment of today’s medical technology – but today is today, and the technology of tomorrow will be a different story. If you want to talk about longevity and mortality rates, you have to qualify your position by stating what sort of applied biotechnologies are available. Longevity is a function of the quality and type of medicine that is available across a life span.
It so happens that most of the advances in medicine achieved over the course of human history, the vast majority of which have occurred in the past fifty years, have solved problems that killed people early in life. Infectious disease, for example, is controlled to a degree that would have been thought utopian in the squalor of Victorian England. The things that kill older people are a harder set of challenges: great progress has been made in reducing mortality from heart disease in the past few decades, for example, but that is just one late stage consequence of the complex array of biochemical processes that we call aging.
The point of this discussion? It is that tremendous progress in medicine, including the defeat or taming of many varied causes of death and disability, has not greatly lengthened the maximum human life span as experienced in practice.