As the author of the Archer bio, I can confirm that -- at least in the prime timeline -- Archer clung to life just long enough to personally witness the launch of the NCC-1701 in 2245, and died peacefully the next day.
I really loved the idea of Archer being there to see the launch of Enterprise NCC-1701. It's a nice homagé to Bones in TNG "Farpoint". Enterprise really ought to have ended on that note, even if it meant Scott Bakula would have had to spend 5 hours in make-up to play a 146 year old.
In the alternate timeline, he held on an extra thirteen years in order to see the maiden flight of the Enterprise-JJ in 2258 -- after which he promptly dropped dead.
The possibility occurs to me that the "Prized Beagle" incident occurred as far back as 2245, just after Montgomery Scott graduated from the academy. Archer lives long enough to banish the Federation's finest transporter specialist to some random world in the starcharts... and then *ahem* accidentally mislabels it Delta Vega!
Makes me happy to imagine all those unlikely coincidences happening at once anyhow...

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