We're not sure that this is common or uncommon.

If the parents were scared by a predator, they may have tried to lure the predator away from the cygnet and return once they felt that the threat was mitigated.

The parents may have been young parents and inadvertantly forgot the young cygnet which is possible, but highly improbable. If the parents were looking for another pond or lake with better habitat resources, the parents may have been scouting for a better foraging or migratory area. More than likely, the parents knew that the young bird was not totally ready for the long flight during the migratory trip. The parents waited to give the young bird a few more days to ready itself for the long trip. The Regal Swan