Core file modification not reported

Yes, you should receive emails for each new issue — though if the issue was already reported in one email, it won’t be repeated in emails by future scans.

In case of email issues, there is a box at the bottom of the Wordfence Options page that says “Send a test email from this WordPress server to an email address” — you can use this to be sure emails are still getting through from your site’s mail server.

-Matt R

That’s a very swift response – thanks.

I’m getting regular emails from Wordfence and some do carry these ‘critical’ notices but not every single one is reported.

Ok – if some of them are still coming through, then it is probably an issue with email delivery by the host. Some hosts have aggressive spam filters or rate limiting on outbound emails, which may prevent some messages from being sent. If you ask the host, they may be able to tell you if some messages were blocked — or if you notice another issue show up in your scan results, but you haven’t had an email about it, the date range may help them narrow it down.

It’s also possible that your host’s IP address is being blacklisted periodically, especially if it is shared hosting and another site on the same server is abusing email — you can check your site’s status on blacklists here, but it might come up clean if the site has been removed since the issue occurred:
https://mxtoolbox.com/blacklists.aspx

-Matt R