Now i see you problem you need the client to redial the broadband dialup connection or else it stays down. Filezilla doesn't seem to do that. TurboFTP has it on the setting tab DUN.
Though this seems more a problem of your isp or pc. That is dropping the broadband connection, that needs fixing not to do it. Magix ftp i'm sure is not dropping the connection, someone look at the magix logs will know more.