I performed the following SQL delete of the postman message logs:
DELETE wp_posts, wp_postmeta FROM wp_posts INNER JOIN wp_postmeta ON wp_posts.ID = wp_postmeta.post_id WHERE wp_posts.post_type = ‘postman_sent_mail’;
It deleted 4817 rows and now it seems to be working again. Looks like the log cleanup task is not running or working.