We looked into this in a screen sharing session. There appears to be a server configuration issue. The session in the root of the folder uses a different session_save_path than the one in the directory we were working on. I'm not sure what could cause that (besides a .htaccess file that updates it and that doesn't seem to be the case for you), but you should be able to take that to your hosting provider for them to fix.
Post back if they tell you what caused it when it gets resolved or if you need more help debugging this issue.