Exim refuses to send and accept email once the server passes the configured load value.
Increase deliver_queue_load_max and queue_only_load in WHM»Exim Configuration Manager»Advanced Editor to a number greater than the server load average. You can check the server load averages in the top right corner in WHM. Choose a number higher than the highest of the three numbers.
If the emails are still not sending, you may need to clear the retry the Exim retry database as well.