Improbable things happen frequently at scale. One possible scenario is just that this card got lost twice.

It could have slipped behind a counter at the original post office and been uncovered when that office was decommissioned 35 years later. Then it would have made its way to a newer sorting facility where either it could have been misplaced again or, more likely, been stuffed in a cabinet somewhere (as I doubt USPS was as adamant about delivering lost mail in the 1950's). That facility could easily be in operation until today - or decommissioned very recently.

No idea if anything like this actually occurred. But at 400M+ letters / day, USPS has the scale for unusual circumstances like this to be somewhat regular occurrences.