> ... the code above was working recently ... What could have changed?

The certificate of the server was changed and the admins have messed up the configuration. From the report from SSLLabs you can see that it reports Chain Issues - incomplete which means that the server fails to provide an essential intermediate certificate which is needed to build the trust chain to a local root certificate.

To deal with this situation you have to provide the missing certificates yourself. This can be done with

my $ua = LWP::UserAgent->new;
$ua->ssl_opts(SSL_ca_file => 'trusted.pem');
[download]

where trusted.pem contains the needed certificates, i.e. the root certificate and the missing intermediate. To make it easier I have provided a pastebin with the all the certificates needed for this specific site. Just save it as trusted.pem.