Staying out of the water longer than in the water is not usual behavior. It is one thing to hang out for 1-2 hours, but not too long. Also, sleeping a lot usually is a sign something may be wrong. You need to capture both of them and get him to the vet to check him for an infection or injury. You must capture her and try to keep them together (or at least keep her out of the pond if he has to stay at the vet's).

The reasoning is that if you take him away from the pond, she is going to walk around looking for him and may get attacked by a predator such as the coyote. If everything checks out and you can return both to the water, you need to so at least 2 hours after dawn since predators will usually go to bed at sun up. If you are concerned about coyotes, realistically, you need to provide a night time indoor shelter, lined with straw, adequate ventilation and inaccessible by predators (i.e., can't crawl into shelter, enter or dig under). You can train the swans to go inside at night. However, you must bring them in at least one hour before dusk and let them out at least two hours after dawn. You may need to change the times slightly so predators don't catch on to what time they enter and exit the pond. The Regal Swan