Following the provided gif file, I have prepared a sample project to test the behavior on my end with the latest version. Indeed, the Selected property value is not serialized at design time for RadDropDownList.
I have logged it in our feedback portal by creating a public thread on your behalf. You can track its progress, subscribe for status changes and add your comments on the following link - feedback item.
I hope this information helps. If you need any further assistance please don't hesitate to contact me.
Dess | Tech Support Engineer, Sr.
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