Well, to be fair, dive ops are sometimes particular about certifications and there is some uncertainty in using a card that isn't readily recognized and can't be checked in an online database.
And organizations that offer training and certification do, IMO, have an implicit obligation to confirm who has and has not received the training and certification they offer. An example would be a four-year degree (B.A., B.S., etc). Institutions granting such degrees keep records in perpetuity and will supply transcripts and copies of the course catalog and degree requirements from the year the degree was conferred, upon request, for a nominal fee.
If the OP's c-card has no modern equivalent, it would still seem to me that NAUI would still have an obligation to replace the card with an identical one, and confirm its validity if asked.
Whether or not some amount of recurrent training is appropriate is a separate question.