Snapshot stalls in media backups

Despite having ensured that all system requirements are met, and all additional constants added to wp-config.php, Snapshot stills stalls, and we see a 404 for the admin-ajax.php file in browser console when that happens.

Each time, it's at the same step, while backing up the 2016/07 media folder, but we can't find anything in there that may be tripping things up.