Would you please provide more details about your exact scenario? If you want to preserve the state of a RadSlidingPane on postbacks, you do not need to write code, this scenario is handled by the splitter itself. You can test this e.g in the following demo:
Expand or dock a sliding pane in the demo and change the skin (this will cause a postback) and you will see that the sliding pane will preserve its expanded or docked state.
In case your scenario is to save/load settings e.g for every separate user, you can use the standard approaches of preserving state in ASP.NET - e.g the same approach as shown in the demo you have linked, Session object, cookies, etc., depending on your exact scenario and requirements.
the Telerik team