You use an Exchange 2010 mail server for 2 or more e-mail domains and have an SSL certificate (maybe wildcard) for 1 domain and its subdomains.
Incoming HTTPS connections are forwarded to your Exchange server, HTTP is forwarded to your Windows or Linux Apache public web server.
Autodiscover for the certified domain works, but not for the other domains.
Exchange allows only 1 certificate to be active at one time for one service, and only Unified Communications (UC) certificates allow multiple top-level domains.
Solutions / Workarounds
Basically, if you don’t want to buy a UC certificate and / or don’t want to include all domains in your existing certificate, you have to redirect the Autodiscover domains to your „main“ mail domain, e.g. your OWA domain.
According to device „never touch a running system“, there might be a ways in Exchange IIS server for redirection, e.g. with additional websites. I have not tested this way because I wanted as few things in Exchange as possible.
Workaround via your HTTP web server: If you are running Apache, you can add this command to your .htaccess file:
Redirect /Autodiscover/Autodiscover.xml https://mail.yourdomain.com/Autodiscover/Autodiscover.xml
Important: If you are working in Linux, note upper- and lowercase letters of the URLs.
Then test Autodiscover with the official MS tool.