The age of 120 appears in various places in the Torah and in our customs, but nowhere are we taught that 120 is an upper limit. So there is no need for concern about a limit to how long technological medical advances may increase human life spans in this world.
Although the Torah states the number of years of Mankind in Genesis 6:3 to be 120, this is actually the number of years that God waited for the world to repent from transgressions before destruction by the Great Flood at the time of Noah. Not a limit to the age of a person.
The Torah relates that Moses lived to be one hundred and twenty years old (Deut. 34:7) and this is the origin of the well-known blessing: "You should live until one hundred and twenty". However, this age is not a maximum age limit, but rather the age when Moses fulfilled his potential in this world. The famous blessing reflects this as something that we should aspire to accomplish with our own lives.
On a lighter note, my wife's uncle always wishes people that they should live to be 122 — so that they should not die suddenly! I’ve also head people jokingly remark that even if the Biblical limit was 120, nowadays if we account for inflation the age limit would be very much higher!
