me.com email not connecting in Mail

I have a @me.com email address that is not working. The grey triangle with the exclamation mark says: Connections to host Automatically added for iOS & OS X Mail on the default ports failed.

I have already deleted the address from my mail account and then added it again, so my Mac is automatically doing the connection settings. I have also disconnected my VPN, to no avail. When I checked the Mail Conection Doctor, I have this message:

For IMAP:

Could not connect to this IMAP server. Check your network connection (Network connection is fine) and that you entered the correct information in the Account Preferences (my Mac did all of this). Also verify that the server supports SSL. If to does not unselect the 'Use TLS/SSL"tick box in Server settings tab of Account preferences.

For SMTP:

Could not connect to this SMTP server. Check your network connection (Network connection is fine) and that you entered the correct information in the Account Preferences (my Mac did all of this). Also verify that the server supports SSL. If to does not unselect the 'Use TLS/SSL"tick box in Server settings tab of Account preferences.

If the Mac set up all my connections am I wrong to assume that it has done so correctly?