I'm finding a problem with the idea that when a dating site is very successful, they lose because the participants immediately become non customers.

The same is true (kind of) with car salesman and real estate salesman, if they are successful at selling the customer a car or house and they do a terrific job, they won't see that same customer again for 8 to 30 years. However, if the customer is delighted, word of mouth spreads, and you get a flood of the customer's friends.