I’m pretty sure the doctrine of that era was that there were always nukes, airborne, 24/7. It served as a deterrent, if the Soviets hit us with a first strike, they knew the submarines and airborne SAC assets would be able to strike back.
Was this a plane that encountered a problem during a training maneuver, or simply while standing ready in the air?
As far as I know, the airborne alert flights continued until about 1965, ending shortly after the refueling midair collision near Palomares, Spain.