Hello!
This last weekend I setup our server as new and to ease the creation of users, integrated with our Office 365 (which to this point has worked fine) and imported the users. This had a somewhat unexpected side effect in that the import used the email address as for the user forename and then synced that change back to Office 365 and so needed to enter this information back in on the dashboard which synced back to Office 365. This may or may not have any relevance to our issue below.
I should also point out that we have our own domain name so within the original Office 365 setup we had just one .onmicrosoft.com user with all the rest setup with our own domain name.
At the weekend when it came to the client install, Outlook (2010 or 2013) would fail on the autodiscover with it asking again for credentials but critically displaying a server name of .contoso.com rather than the office365srvr.contoso.com . As I mention, Office 365 had been operating fine for some time and DNS records where checked and have been set for sometime. I spoke to Office 365 support and after a while come up with a temporary solution (so that I could complete the client installs) of assigning each user a onmicrosoft address, using that in the new account wizard to pick up the server correctly and then signing in the the Office 365 .contoso.com credentials.
This worked OK to get us past the weekend (although I am having to reset up profiles on quite number of users where they get disconnected but with no credentials box appearing) but isn't a solution. The clients do not see public folders or their archives and of course we don't want to keep having to reset the profiles.
I'm think that there must be something in the internal network that needs reconfiguring but I don't know what. I have tried pointing the client to an external DNS server just in case the internal DNS server was throwing the autodiscover out but this has made no difference.