The simple explanation is that lead sulfate is formed initially as a metastable amorphous precipitate, which then slowly converts to a crystalline form that is stable.
The amorphous form has a large surface area and can be electrochemically converted to lead readily.
The crystalline form has a much lower surface to volume ratio and its electrochemical conversion back to lead is extremely slow. (See:
https://en.wikipedia.org/wiki/Sulfation)
Such dissociations between kinetics and thermodynamic equilibriums are common.
One example is dissolving sugar in water. If one takes 50g of sugar and adds it to 50 mL of water, it will take a long time to dissolve. Once dissolved, however, it will not come back out of solution unless highly concentrated over a long time (e.g., crystallization of honey). Polysaccharides (e.g., agar) are particularly prone to such behavior.
That is the simple explanation, but it is not the whole story. Another contributing factor seems to be the formation of mixed salts, such as "tri-basic lead sulfate" and "tetra-basic lead sulfate". These are solid forms that contain relatively stoichiometric mixtures of lead sulfate and lead oxide in different ratios and water molecules. The behavior of such salts is complex and of great current research interest in the production of long-lived batteries. (Here are two references those interested can use to find the primary literature:
https://www.osti.gov/energycitations/product.biblio.jsp?osti_id=599910 and
https://en.wikipedia.org/wiki/Lead_sulfate)
When one considers that lead-acid batteries have been around for about 150 years, the complexity of the chemistry of sulfation is revealed by the recency of those studies.
The bottom line seems to be the inexorable march of the "amorphous" lead sulfate that is initially formed (whatever its actual complex composition) to a much more stable crystalline lead sulfate.
Maybe with more detailed knowledge of the chemistry, long-life lead-acid batteries will be developed. In the meantime, my BS detectors are triggered by claims of desulfation using pulses at some "resonate frequency" of lead sulfate or by adding secret rejuvenators to the dead cells.
The Fountain of Youth has yet to be found -- either for old batteries or old people.
John