I guess it depends on what's meant by "band" - the Kingston Trio, who are still touring, have been around since the late 1950s, but there is no one now with the group who was in it when it was founded, although the name continues.
Ditto the Limeliters - no original members are left, but the group name continues and they still tour.
And, of course, ditto the Vienna Boys Choir, whose membership has changed constantly over the past 70-80 years!
Peter, Paul & Mary have always performed with the original three members, although since Mary's serious illness Peter and Noel sometimes perform as a duo. I think they started in 1961-62, so 48 years.