When I open the webinterface to my mailserver (Zimbra) through HTTPS, I get the message that the 'signing certificate authority is not known'. In Geary the same thing happens. But not in Firefox or Thunderbird. The certificate is valid and not selfsigned, it's a Comodo PositiveSSL certificate.
I think this is most likely an issue with
glib-networking as reported in another related question about SSL handshakes failing.
Try doing a manual connection via the terminal next time this happens using the openssl command as shown below, then share the results.
openssl s_client -host mail.myzimbraserver.com -port 443