We haven't had a problem since we started using parchment paper. My guess is moisture/grease from the pizza was soaking into the stones and weakening them over time.

You're almost certainly correct.

As an aside, I once set the oven on self-clean, forgetting a pizza stone was still in there, and that was a mixed experience. On the one hand, I had to open the windows and pull the smoke detectors as smoke poured out of the oven for a while. On the other hand, when done, the pizza stone looked like it was fresh out of the box, not a stain on it.

I have no idea if that's a plus, a minus, or meant nothing for that particular stone... but it eventually cracked like the others.