Another option, which has the advantage that it will still work properly if the script is interrupted and restarted, is the storable module. This will allow you to easily save variables as a file and retrieve them later, like a very crude database. It might look something like this:

use storable;

my $results = retrieve('results_store');

sub check_site {
  my $domain = shift;
  my $current_result = check_domain($domain);
  my $last_result = $results->{$domain};
  if (($last_result == 200 || !$last_result) && $current_result == 400
+) {
    send_email($domain);
  }

  if ($last_result != $current_result) { 
    $results->{$domain} = $current_result;
    store $results, 'results_store'; 
  }
}
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