taking it close to TOS would mean most of the Enterprise crew would be dead of old age!
T'Pol was still alive after being thrown back 117 years (EČ
) and lived well into the 2250s in "A Less Perfect Union". The same story mentions Elizabeth Cutler as the second-last survivor of the NX-01.
Archer lived to see the launch of the NCC-1701, presumably in both ongoing timelines (April's Enterprise
in New Trek). Lieutenant Commander (retired) Hoshi Sato died at the hands of Kudos (In a Mirror, Darkly).
(not necesarrily canon)
People have a long life expectancy in the future. See butt-kicking Elias Vaughn, a centenary.