Was it ever mentioned or made known how long Captain Archer lived for? I am sure I read something saying he died sometime in the 23rd century.
Yes, in the reboot timeline
In the prime timeline, neither the timing nor the general circumstances surrounding the death of Jonathan Archer are addressed in the television series or films.
However, in the 2009 film Star Trek, Scotty mentions losing
"Admiral Archer's prized beagle"
in a transporter experiment. Screenwriter Roberto Orci confirmed the identity of this "Admiral Archer" in comments at the web site Trekmovie.com, a Star Trek news site that Orci frequented (until he made heated comments on the site towards Star Trek fans in the weeks following Into Darkness):
yes, it is, Admiral Archer is a reference to the Archer we all know and love, and yes he would be over 100, which is a likely life expectancy in a futuristic space faring race of humans as depicted by McCoy’s (Deforest Kelley) in THE NEXT GENERATION.
Therefore, in the reboot timeline (post-Nero), Archer did live well into the 23rd Century.
If we assume that Nero's incursion had little impact upon Archer's life, then he would have lived into the 23rd Century in the prime timeline too, but there is no independent confirmation of this.