Yes I have noticed that the problem is only related to sites that have authentification. So for example hotmail.com (https://hotmail.com) will not work either.
What I can't understand is that the script works fine whichever site I choose to parse.
But when I package the script it only works with none secured websites. For example www.google.com will get parsed by the packaged script (.exe)
I debugged and the process stops exactly when I call the https site i.e. at line:
# Connect to the login page
my $response = $bot->get( 'https://anyURLwithCredentials.com' );