Does Archer actually go on any more missions after he makes that speech? Reed and Mayweather said that they would stay with him because they believed it wasn't his last voyage into space. Or did he retire?
Archer is listed as Admiral on various different sites
Archer's fate is revealed in the episode "In a Mirror, Darkly Part II" when a computer information screen aboard the 23rd century Starfleet vessel USS Defiant is briefly visible. According to the computer profile, Archer was an Admiral and Chief of Staff at Starfleet Command at the time of his retirement. He later went on to serve as ambassador to Andoria from 2165 to 2175. From 2175 to 2183, Archer served as a member of the Federation Council, followed by eight years as Federation President (2184–2192). He was also an honorary member of the Andorian Imperial Guard.
That was from his wiki page done with a simple search.
Also From Memory Alpha page about Archer
No date was given for Archer's retirement from Starfleet. For the biographical display seen in "In a Mirror, Darkly, Part II", writer Mike Sussman wrote a final section of text that didn't end up being visible on screen, stating that a 132-133 years old Archer " … died at his home in upstate New York in the year 2245, exactly one day after attending the christening ceremony of the first Federation starship Enterprise, NCC-1701". Note that Sussman himself has said this information might not be canon.