Ensure that your SSL virtual server  has it’s IP address  set to All Unassigned.

How is your SSL virtual server  configured - anonymous and windows
integrated, or just basic authentication? Do you have an
http://<computername> specified in the alternate URL page?

I've seen search  problems with SSL if their is no windows integrated
URL configured for the portal.

Make sure that you have the certificate  installed correctly. When you browse to the site, make sure that the cert name is the same as the address  of the site, etc. Basically you need to ensure that you aren't getting and intermediary ssl  prompts warning you that the site  name doesn't match the cert name, etc. You should just type in the https  address and it will take you directly to the page without any prompts except the login prompt.

Our portal default  address is https://server_name and the
alternate is https://sharepoint.domain.com

Our IIS is configured to use integrated authentication with Anonymous
Access on both the ddefault website  as well as the central
adminitration website. We are able to access  the portal site  without
a problem using https://servername and also
https://sharepoint.domain.com.

When the full  update is run on the content  sources, this is the error
that is registered in the gatherer  log. The address  could not be
found, (0x80041223 - Error found  in the Secure Sockets Layer (SSL)
certificate sent by the server. )