s2Member will never prevent an admin from having access, so there's something else going on. Most likely a session thing.
Are you using the s2File shortcode to get the link to the protected file? Or how are you linking to it?
Could you verify thta you're not mixing www and without in the URLs? https://www.s2member.com/forums/topic/dont-mix-www-and-without/index.html
I look forward to your update.