I would check the return code of each $ftp->... call just in case something wrong is happening:

use strict;
use warnings 'all';
use Net::FTP;

my $host = 'ftp.ncbi.nih.gov';
my $ftp = Net::FTP->new($host, Debug=>0)
  or die "Cannot connect to $host ", $ftp->message;

$ftp->login('anonymous', 'anon@anon.com')
  or die "Cannot login ", $ftp->message;

$ftp->cwd('/refseq/LocusLink/')
  or die "Cannot cwd ", $ftp->message;

$ftp->type('binary')
  or die "BINARY failed ", $ftp->message;

$ftp->get('LL_tmpl.gz')
  or die "Cannot get file ", $ftp->message;

$ftp->quit; # well ... almost every call ;)
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Take a look at the Net::FTP docs.