If technological progress continues exponentially (including increases in human or machine intelligence to make them possible) then our understanding of biology and life-extension will continue to increase, and many such life prolonging-treatments will be made available to the public.
If one life extension makes you live 5 years longer, and during that time an new one comes out that lengthens your life by a few more years, you can see how one might keep "catching" these just in time and thus gradually transition from mortal to immortal.
If you live long enough, you may eventually live past the point where science makes it possible to live forever. For most of us, this is impossible because we lost the birth date lottery.