I see no scientific reason a human couldn't be modified or engineered if not to be effectively immortal, barring accidents, to at least last several centuries in good health, barring traumatic accident, or an exceptionally virulent infectious disease, until further advancements could make it true immortality.
Genetic modifications on lab animals has double or tripled their life span already. And one can presume that lab conditions in terms of cleanliness, the absence of predators and accidents, the animals were living longer than their wild counterparts already.
Do I think serious life extension is as simple as simply lengthening the telomeres on our genes, or creating a mechanism to lengthen them each time a cell divides? No, it'll be more complex than that. There are many human cells and tissues that are programmed to only divide a certain number of times, and those would have to be addressed, without turning into tissues that never stop growing, or some kind of cancer...
And there's probably dozens of biological mechanisms or complex systems that run-down and age in our bodies. Although if they didn't start turning up until after I was 90-100 (and in a body that didn't age much past 40 or so until then...) I'd take the chance. Tuning them all, and the unintended side-effects will be complex for sure.
It certainly poses lots of interesting questions, even if everything works perfectly biologically, what happens to a person after X-hundred years of existence to their cognition, to their memories? Do older and older memories fade and get re-written in around a 100-odd year "window", does the brain lock up, or go insane?
However, I see no real fundamental scientific reason that effective biological immortality is impossible.
Although post-human machine storage seems "easier". Brain/computer interfaces need only be designed for that, still a huge challenge, but we've already got some progress in that in terms of ECG,s', MRI's, experimental vision systems, and brain controlled prosthesis. It also negates any Malthusian problems that may/will happen in terms of population and physical resource/space needs.