Let me refresh your memory.
The plane experienced a catastrophic failure of the rear pressure bulkhead, which damaged hydraulic and other control lines to the elevators/rudder. I do not believe the plane lost it's vertical stabilizer; they only lost the ability to control the plane.
You are correct that they kept it in the air for a substantial period of time, this was acheived by changing power settings to compensate for aerodynamic forces acting on the plane.