irules and session cookies

To answer your question try this (where mycookie is set to your cookie name, and Path is set as appropriate);-

when HTTP_REQUEST {
    set fInactive 0
    if {[string tolower [HTTP::path]] eq "/vdesk/hangup.php3} {
        set fInactive 1
    }
}
when HTTP_RESPONSE {
    HTTP::header insert Set-Cookie "mycookie=xx; Path=/; Expires=Thu, 01 Jan 1970 00:00:01 GMT; HttpOnly"
}

However why don't you try setting the cookie expiry to 20mins? The Expires attribute will be updated each time you access the site - it will act as a parallel inactivity timer.