I have following simple code:
<%@ Page Language=\"C#\" AutoEventWireup=\"true\" CodeBehind=\"testForm.aspx.cs\" Inherits=\"Orbs.testForm\" %>
This question covers all the possibilities better than other posts out there, so I'm adding this explicit answer. In my case @Edyn's comment worked, even though the original problem already has this:
Set ViewStateMode="Enabled"
on the dropdown control itself.
I also set it on the page declaration at the top of the page, just in case.
This is .Net 4.0, so perhaps something was changed (but certainly not fixed nicely).