The problem is probably a predatorial one. Raccoons, opossums, snakes, rats, turtles, and ants will eat eggs. Raccoons and turtles are notorious for raiding bird's nests for eggs. Incubation should be undertaken only by a professional as it is hard to incubate a swan's egg, if it explodes it can do major damage, and finally, the birds will imprint on you which is not good.

The best thing that you can do for the swans is to build a pen (1/2 in the water and 1/2 on land, made of fencing which cannot be dug under or crawled into from above. Think of a large dog fenced dog run. You need to protect the swans and their eggs from predators and enclosing them in the above described pen with a feeder inside the pen, should help with the disappearing eggs.

Now, having said this, if there is something wrong with the egg, the parents will take it out into the water away from the nest so that predators will not be attracted to the nest. The egg will be discarded in the nearby water. The only way to know for sure is to try and mount a camera near the nest and see if you can capture what is occurring.

If the cygnets are dying because they are not eating, there is either something inherently wrong with them (i.e. defective), or there is a parasitic, fungal or other infection or possible deficiency in their nutrition which causes them to lose their appetite. Swans need cracked corn and poultry layer pellets for nutrition. Cracked corn provides Vitamin A, which is needed by the birds for neurological purposes and also acts as a filler so that the swans do not feel hungry. It helps beef them up. The poultry layer pellets provide micronutrients, minerals and vitamins need by the swans to address daily nutritional requirements. There must also be plenty of aquatic or other vegetation in the habitat. If not, lettuce should be provided. However, for the cygnets, the lettuce needs to be finely chopped. The Regal Swan