I have a cookieless web application based on asp.net 4.5.
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Thanks to @AdrianWragg, I found it! The redirection was done through a reverse proxy but this server had an ISAPI filter that was removing the session Id from the request, after I removed the ISAPI filter everything worked just fine.
Can you try to change your configuration in the web.config to:
<sessionState mode="InProc" cookieless="false" timeout="10"/>
?