I always forget exactly what I need to do to implement IPostBackDataHandler correctly, so I'm tracking the steps here for future reference.

1. Implement the IPostBackDataHandler interface.
2. Override OnPreRender call Page.RegisterRequiresPostBack(this);.
3. Override Render and write the form fields you need posted back.
4. In LoadPostData, grab the data you posted back.  The postDataKey arg is the same as the ClientID and is generally not useful.