By default the RadTeeView persists its selection across post-backs and it's not necessary to store its state explicitly . Could you please elaborate a bit more on the exact scenario that you are trying to implement and why the old node selection is not persisted?
If for some reason the selection is lost you can store the lastly selected node in hidden field for example, retrieve that node by using the RadTreeView client-side object method findNodeByText(string text) and select it explicitly. Please find in RadTreeView object client-side API article
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