This can be any chronic disease you can think of, and these must be ruled out in any examination. I would look at providing a balanced diet in the form of pellets or crumbles. And I would remove the nest box for the season if she hadn t laid her fourth egg on time, to diminish the reproductive drive. I hope my answer provides some practical advice for you. He is approximately 10-11 years old and in fine health.
Birds generally handle transport remarkably well.
If you can freight him in his own cage that would be great, as he would be very comfortable in his own environment. However, freight companies have strict criteria for strength and size of transport containers and sometimes the bird's general cage will not be safe for transport. Transport containers should be sturdy enough to survive dropping and packing. They should be closed in on all sides, with an open front for ventilation. On long trips water should be provided by wetting cotton wool in fixed containers.