I had a similar issue with my SSL pages having redirect loops after auto-updating to WordPress 3.8.1. As fktc suggested, previously I had made changes to my functions.php file, specifically modifying is_ssl() to check if HTTP_FRONT_END_HTTPS was set to ‘on’ and that change had been reverted. Updating the code so it correctly detected if SSL resolved the redirect loops.
I am encountering the same issue with my site. Did you find a solution?