Turtles, egrets, owls, hawks, largemouth bass and any number of other predators can kill the young cygnets as well as disease, toxins, parasites, etc.

If the male is walking with a balance problem, you need to get him to an avian veterinarian ASAP. He may be suffering from ear mites or other parasites, or have an infection such as encephalitis or poisoning of some kind which all can be lethal. These types of anomalies can sometimes be prevented with vaccinations or other medications once you know what the male may be afflicted.

As far as making it safer for the cygnets, you may have to pen the nesting parents next year in an enclosed pen (top to bottom) so predators cannot access the pen. The pen must be 1/2 in water, 1/2 on land, with zero entrance, no steep banks, nesting material on the land part of the pen, and a feeder inside the pen). You will also need to cover the outside perimeter of the pen from the bottom rail to 4 feet high with poultry fencing so the cygnets cannot get out of the pen. You will need at least a 12 x 24 foot pen and keep the family inside until the cygnets are 4 weeks of age or the size of a small duck. This will prevent some of the predators such as egrets, fish and turtles from getting to them. The Regal Swan