Figured it out. Instead of using <telerik:RadAjaxPanel...> you need to wrap it in <asp:UpdatePanel...
Example:
<asp:UpdatePanelID="UpdatePanel1"runat="server"> <ContentTemplate> <telerik:RadSplitter ID="RadSplitter1" runat="server"> //Do stuff </telerik:RadSplitter> </ContentTemplate></asp:UpdatePanel>