I think they take the biometric reading when you first activate the ticket and then use that reading each time you enter a park again.

FWIW - I don't know if it's really a fingerprint. My husband and I often "test" the machine, since our hands are about the same size. We switch tickets and still get in using our own finger.

I would imagine the reading is erased after the last park closes on the last day of your ticket validity.