Unbaked clay tablets tend to simply disintegrate. Those at Knossos and Ninevah were baked by fires that destroyed the buildings in which they were housed. Mycenean tablets appear to have been reused each year, so the 'expiration date' in that case was man-made rather than imposed by the material.
Papyri have also survived more by good fortune than by design, being preserved in tombs and rubbish heaps. They lay undisturbed in an environment where the temperature and moisture content of the air remained stable over time, in a range conducive to the survival of the material.