There are a couple of possibilities in this situation.

1. A predator is carrying the eggs from the nest. However, if you have not seen any disturbance in the eggs (cracked, etc.) this possibility could be ruled out.

2. The most probable cause is that the young swans have never laid eggs and have no earthly idea what to do with the eggs. The young female is dropping eggs as she feels the need to do so and has no idea that she should be dropping the eggs in the nest.

The eggs are probably not going to survive as the female has no clue that she must sit on the eggs. This egg laying process the first year may or may not be successful, depending on if the swans learn real quick that they must sit on the eggs. So, placing the eggs back into the nest is only going to attract predators which may harm the juvenile swans.

Additionally, even if cygnet(s) are produced, they may be lost during the first year because the parents will not care for them as the parents do not know how to care for the offspring. We have seen first time swan parents go through the mating/nesting/egg laying/hatching and production of offspring with no problem and they are great parents first time out. Then, there are other occasions like your swans, that have no idea what is going on and it may take them 1-2 years to understand the process and what they must do to bring the eggs to viability as well as care for the offspring to maturity. The Regal Swan