By the time children today are old enough to die from natural causes, we'll have a cure for that.
At some point I think we will 'cure' cellular senescence. Then humans can stay physically in their prime, indefinitely. But there are other limits, like memory. Because memories require physical space, there is only room for a limited amount.
I think we can get past that either naturally, by overwriting old memories, or artificially, by augmenting memory with technology. Research is already looking at brain augmentation with electronics.
So what will be the ultimate limit? Or will humans achieve immortality?
Cellular senescence includes the arresting of a cell's life cycle without undergoing cell death, essentially cells would not deteriorate and not die unless (depending on how the scenario is set up) acted upon by an outside force.
I can partially agree that if medicine is advanced enough at the time and well tested they would undercover most of the short term issues during clinical trials.