Custom RadioButton loses Checked value on PostBack

I am creating a control that inherits from the RadioButton, so that I can set the GroupName property manually.  Everything is working okay apart from the fact that when the page posts back, the RadioButton becomes unchecked if it has previously been checked.
This is the first time I've tried inheriting from controls, so must be doing something really silly.  I would welcome anyone helping me to improve my code so that the control's Checked value persists through postbacks.  Please note that I am causing a postback using a button, not the actual RadioButton itself, if that makes any difference.
Here is my code:
 
Imports System Imports System.Collections.Generic Imports System.ComponentModel Imports System.Text Imports System.Web Imports System.Web.UI Imports System.Web.UI.WebControls Namespace myNamespace.Web.UI.WebControls <DefaultProperty("Text"), ToolboxData("< ...