You're not setting $i anywhere that I can see. You might be better off with something like this:

foreach $i (0 .. $#initList) {
    $command = <<eod;
ftp -nv $rem_host << eof > $log;
user $rem_user $rem_passwd
mput $ftp_source_path[$i] $ftp_dest_path[$i]
bye
eof
eod
}
[download]

But I really think you'd be better of using Net::FTP.