I bet the clay tablet will be just fine. No word on moldy cards.
Whenever a city was conquered, the tablets there were immortalized as the city burned down. But cities that didn't get sacked didn't burn down, and their tablets could be lost. For example, we don't have the clay records from Hammurabi's reign in Babylon, because (a) he was a strong king, and Babylon wasn't conquered on his watch; and (b) he reigned a long time ago, and that period of Babylon sank below the water table, dissolving all the records.
[1] Some tablets were intentionally fired for posterity.