Old webinator sets the login cookie via a <meta> html tag instead of a HTTP header, which modern browsers no longer support. So after you log in you see a successful page, and your browser doesn't keep the cookie around for the next request - which tells you to log in again.
Using IE for the admin interface is a fine workaround, or you can update to the latest version which has this fixed.
Using IE for the admin interface is a fine workaround, or you can update to the latest version which has this fixed.