I add a line of code like this
Page.EnableViewState = true;
Did that fix it for you?
Its true this module does postback but it does ajax postback using UpdatePanel so it doesn't interfere with other content modules on the page.
I'm not opposed to adding that line of code if it fixed it, but it works for me so I think something is different on your environment.
The MS AJAX dll, System.Web.Extensions.dll is included with the source but if you have installed a different version on your machine using the installer then the version in your GAC may take precedence over the one in the bin folder and this could be a factor. Maybe you have an older version in the GAC.
Also if you are using a custom skin maybe you don't have this in your layout.Master:
<asp:ScriptManager ID="ScriptManager1" EnablePageMethods="true" runat="server" />
Hope it helps,