Archer lived until 2245 and backstage notes suggest that Denobulans are a long-lived species, though nothing on exactly how long. Of course it depends on what age he was when onboard the NX-01, given all his qualifications and experience he could well be older than T'Pol.
Archer is still alive in the Kelvinverse. Guess Nero's incursion also had an effect on modern medicine as well. Incursion date 2233.04. Scotty tells Kirk he was sent to the Delta Vega outpost after transporting Admiral Archer's beagle. In 2258. Hahaha
I'm guessing Vulcan medicine is why humans live that long in the Trekverse. Well... that and whoever's writing the story that means sometimes 75 is retirement age, Kirk has a midlife crisis at 50 and sometimes 120 is an easily achievable age.
It was never established that was Jonathan Archer, could easily be a descendant or someone unrelated (Archer isn't an uncommon name).
Answer, However long the plot needs him to be! Bassically it was "a long lived" species, so, I'm guessing longer that an average human, maybe not as long as a vulcan, I belive Phlox stated that being away from family was okay because they had a long life with plenty of time to see them. So, lets play Disco Easter eggs, They could show Tpol, and T'pau, show Phlox. The humans would be dirt old, even Hoshi would be 110 -120. Maybe a line with "insert communications officer name" and say he spent a semister with Hoshi at her amazon school in the academy maybe.
Oh, Archer is long dead and buried. It's the average beagle lifespan that has skyrocketed in the 22nd century and beyond! Timoi Saloniemi
In a based of Phlox's knowledge, i guess that Denobulans are long-lived. Try to imagine how many books Phlox had to read and how many time it had to take care of it. I think much more than hundred years
Some of Phlox's dialogue about his grandmother may suggest that last war occurred when the grandmother was young, before either of Phlox's parents were born.
https://memory-alpha.fandom.com/wiki/Valerie_Archer Valerie disagrees! Oh wait. She's species 8472. You may be on to something.