Exchange 2013 co-exsting with Exchange 2007 Prompting Clients for Authentication

Can you post the headers for that request and response here? What auth scheme is your Autodiscover configured to use? Are the 401s coming from the same CAS that the original request went to, or a different one?

There's a section of the pool assignment iRule created by the iApp that works around repeated auth prompts for Outlook clients by disabling OneConnect and the NTLM profile. I'm wondering if it could apply in your case, with a change of criteria:

when HTTP_RESPONSE {
    if { [string tolower [HTTP::header values "WWW-Authenticate"]] contains "negotiate"} {
        ONECONNECT::reuse disable
        ONECONNECT::detach disable
        NTLM::disable
    }
        if {[HTTP::header exists "Transfer-Encoding"]} {
        HTTP::payload rechunk
    }
}