Even bits of Concorde's tail "fell off" a few times.
BBC NEWS | UK | Part of Concorde tail 'fell off'
27 November 2002: New York flight loses part of lower rudder
8 October 1998: Part of lower rudder detaches off Newfoundland
21 March 1992: Large section of upper rudder lost at twice speed of sound
4 January 1991: Portion of upper rudder separates during London - New York flight
12 April 1989: Part of upper rudder detaches at 44,000 feet
The old girl(s) survived all these - Tough as old boots.
Flying Lid