LWP::UserAgent defaulted to verifying SSL connections with 6.00, so if you can connect to one site and not another, it's likely a certificate issue.

If you're sure that the site can be trusted despite a bad certificate (or you just don't care), you can override this behaviour in ssl_opts.

my $mech = WWW::Mechanize->new(
  ssl_opts => { verify_hostname => 0 },
);
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