As has been already advised the URL in your script does not match the URL in your description. Fixing it gives this SSCCE which runs to completion with no errors for me:

#!/usr/bin/env perl 
use strict;
use warnings;
use WWW::Mechanize;

my $url  = 'http://www.csbio.sjtu.edu.cn/bioinf/MemBrain/';
my $mech = WWW::Mechanize->new;
$mech->post ($url);
die $mech->status unless $mech->success;
[download]

You can run this code for yourself, confirm that it works and then start to expand it from there. That might be easier for you that trying to condense what you already have into an SSCCE.