How to fix when Apple Mail fails to display new Exchange Imap e-mail messages?
Have a look at the Microsoft Exchange Server.


First verify that the "Microsoft Exchange IMAP4" service is started.
Secondly verify that the Exchange IMAP virtual server is running. Therefore start the Exchange System Manager application, and open the path "Administrative Groups" > "First Administrative Group" > "Servers" > Server > Protocols > IMAP4.


In our case the "Default IMAP4 Virtual Server" repeatedly stopped itself.

After starting the "Default IMAP4 Virtual Server", the new mail started arriving in the Mail.app application.