The Concorde tyres were obviously under enormous stress. The only other Aircraft that I can think off whose Tyres have such a hard life (on landing only of course!) are those installed on the Space Shuttle.
Not sure how the landing and takeoff speeds compare, but the SR-71 tires had the additional disadvantage of a prolonged heat soak to far higher temperature than any large Concorde component, I think. Sources say the tires were good for 15 cycles, other say 6, and attribute two early hull losses (64-17950 and 64-17954 in 1967 and 1969) to tire failures progressing to magnesium wheel fires propagating into the rest of the airframe.