The fact that you can change the PdfDocumentSource from a static button shows that the problem is not with the RadPdfViewer but something with your logic / UpdatePanel.
1. I think it is not necessary to put RadPdfViewer in UpdatePanel as it does not need postback in order to load a different document.
2. You can try to change the DocumentSource from user interaction, not from the postback. This may solve the problem.
Hope this answers your question.