First, we have to ask if someone maintaining the grounds might be taking the cygnets to control the population? Have you asked: "If management endorses the swans having cygnets? Is management removing the cygnets? What does management plan on doing with the cygnets once they are full grown?"

Once the cygnets reach one year of age, the parents will chase them from the area, so if they do not have another area to go, management will need to find them a good home. In many cases, it is the management of a facility that does not want to deal with babies of any kind and they will sometimes remove the young so there are no maintenance/care issues.

Second, with what you describe, if human intervention is not the cause, then predators are the likely cause. When cygnets or ducklings are couple weeks of age, predators such as large mouth fish, turtles, bull-frogs, herons, egrets, owls, hawks, otters, raccoons, mink, alligators, etc. will take them.

As they get a little larger, such as the size you describe as being small duck in size, then this starts to limit the predators that can eat something that size. Usually, snapping or soft-shelled turtles, otters, minks, raccoons, owls, hawks and alligators are your probably culprits

Third, if predation is not the cause, then other issues may come into play such as disease or nutritional concerns if the swans are not fed supplementally (1/2 cracked corn with 1/2 poultry layer pellets and lettuce). So, as you can see, there are many reasons that the cygnets may be disappearing. The Regal Swan