Have you tried turning on debugging to see the communication with the server?

my $ftp = Net::FTP->new($host, Debug => 1);
[download]

The main thing to look at is what command Net::FTP is using to get the size and what the server returns for that command. Newer FTP servers support the SIZE and STAT command which are more reliable than doing a directory listing and parsing the results. Especially since the format for directory listing is not standardized. If the FTP server is running on something other than Unix, it is quite possible that the dirctory listing doesn't contain the size or doesn't contain it in the right place.

Try connecting to the ftp server manually. Try doing a SIZE command or STAT command to see if it supports it. Try doing a "dir" and see what the format looks like.