I wonder what libbyapp.com is doing that the plugin can't imitate (both for staying logged in and for downloading). I'd have thought there's a way watching network traffic and then simulating it (something I'm not good at), but I guess it's doing something odd or complex.
There are projects to capture cookies from a site, such as
https://github.com/borisbabic/browser_cookie3 and
https://github.com/thewh1teagle/rookie and even selenium for imitating a browser. Is there some other security thing libby is doing?