Net::SSL::ExpireDate constructs the SSL handshake by hand and explicitly does a TLS 1.2 only request with only a handful of ciphers. It might be that the site you are trying to reach does not work with TLS 1.2 or does not support the ciphers offered by Net::SSL::ExpireDate. I would recommend that you instead use a library which is commonly used to establish SSL connections and which should work with almost every site. With IO::Socket::SSL you can get the expiration date like this:

use strict;
use warnings;
use IO::Socket::SSL;
use IO::Socket::SSL::Utils;

# ignore certificate errors since we only want to get the expiration
# time and not transfer any sensitive data
my $cl = IO::Socket::SSL->new(
    PeerAddr => 'www.google.com:443', 
    SSL_verify => 0
) or die "connect failed: $!, $SSL_ERROR";
my $cert = $cl->peer_certificate or die "no peer certificate";
print "expire=".localtime(CERT_asHash($cert)->{not_after})."\n";
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