A microcontroller in sleep state (or similar) draws extremely low power, micro or nano Amps. It only wakes up when it sees data on the card reader, reads the card reader data, and decides if it should open the lock. The motor that unlocks the door only runs for less than a second. Then the whole thing goes back into sleep state.

Hotel doors are only opened 10s of times per day, at most. A pair of couple Amp-hour batteries will last quite a while. Maybe replace them once a year. Tech with an electric screw driver maybe takes 1 minute per door, even a 600 room hotel only costs 2 days of labor once per year (max 1 week, if the tech is slow). That's not that expensive. And the tech's time is 10x the cost of the batteries, coin cells in bulk are dirt cheap.

(Note: This is all specific to Onity locks)

Also, is it the housekeeping staff that reprograms the lock after they clean the room? It seems like it would be very inefficient to send a special person around to reprogram the lock after every check out.

As for reprogramming the doors, that only happens very rarely. The cards have an expiration date and a code that cycles, meaning that when a new card is introduced, the old ones won't work anymore. So really it only needs to be reprogrammed when the clock gets out of sync or the batteries die (there's no non-volatile storage, just RAM).

How interesting. Does that mean that you could theoretically have access to an empty room if there's no new occupant? It seems like you need some sort of expiry to prevent that from happening, but I can't imagine how that would work without some signal passing between the front desk and the lock.

You can't make cards out of nothing, though, so that helps mitigate it.