Since downgrading to WordPress 3.5.2, I have not had any issues. I have left a browser tab open that has the WordPress Write Panel open as if I was editing the post. I've left it alone for a few hours and I have yet to see the Server Disconnection warning. I've also had YSlow running the entire time and have yet to see a POST Admin-AJAX.php request time out. It's not conclusive just yet but it's a step in the right direction.