When we run OOF in Outlook 2007 in the company network or via vpn, everything worked. However, when we simply connect to our Exchange 2007 SP1 rollup 2 from the Internet using RPC over HTTPS, we got the "'Your Out of Office settings cannot be displayed, because the server is currently unavailable. Try again later." message.
And doing the 'Test Email Autoconfiguration' from CRTL-System Tray failed with the message "Autoconfiguration was unable to determine your settings", and the Log tab shows:
"Autodiscover to https://company.net/autodiscover/autodiscover.xml
"Autodiscover to https://autodiscover.company.net/autodiscover/autodiscover.xml
Of course, there is no A record 'autodiscover' specified in our DNS for company.net domain. Is that the main problem? And the DNS record for company.net points to our www site.