I am very happy to announce that (as far as I can tell) all of the email delivery issues are now fixed.
Those who know anything about such things might be surprised to know that the issue was fixed by moving the forum DNS records to a new provider.
It seems that the previous company hosting the DNS (who have had a major restructuring in recent months) had done something that caused the DNS public signing key records to be frequently corrupted, causing the authentication of emails to fail.
Thanks to JohnD for helping with testing the problem.
Email delivery issues
Moderator: myglaren