While the Space Shuttle fleet's computers were indeed upgraded slightly in 1991 the general point stands about upgrades. You're mistaken about the hardening aspect though. The Space Shuttle used a descendant of the System/360 called the AP-101. It was an avionics computer used in a number of aircraft including the F-15. The Space Shuttle used a fly-by-wire system so instead of mechanical linkages between control surfaces and the engines the cockpit just sent electrical signals to the flight computer and it then sent signals to the various components and told them what to do. The flight computer also relayed sensor data back to the cockpit.

As with most aircraft the Space Shuttle's flight computers didn't need to be upgraded often. The Shuttles themselves weren't getting new parts all the time nor was physics changing a whole bunch during their operational lifetime. When they were replaced in the 90s in the fleet it was to upgrade them from the original ferrite core memory to semi-conductor memory. Pretty much everything else about the computers remained the same.

The Shuttle's computers were naturally hardened in that they did not have super small electrical traces to begin with. High density circuits are more susceptible to radiation events than low density circuits. The Shuttle's computers had 32k words of memory if I recall correctly. The other aspect of their hardening came from software design and redundancy. The Shuttle's avionics software was itself redundant and was designed to handle errors gracefully. It would need this capability even if radiation wasn't an issue because flying is difficult. The computers were also run in parallel to provide physical redundancy. If the computers ever disagreed on calculations majority ruled and the disagreeing unit would signal to the crew that it had become unreliable and the fifth hot spare could be brought online.