Assuming it's a history issue, could you rework your script to create a new agent for every loop?

i.e.:

#!/usr/bin/perl

use WWW::Mechanize;
use Devel::Size qw(size total_size);


while (1) {
  my $agent = WWW::Mechanize->new();
  
  $agent->get(qq(http://www.yahoo.com));

  print "agent size = ".total_size($agent)."\n";
}
[download]

I admit, I have no idea how fast or slow the WWW::Mechanize constructor is.