There appears to be an issue with email delivery from Healthchecks.io, we're looking into it.
The SMTP relay service we're using has acknowledged and is investigating the email delivery issue. We are waiting on updates from them.
Email delivery has resumed, and has mostly caught up with the backlog of unsent messages.
If you've just received a number of email notifications from Healthchecks.io, be aware that some of the notifications may be significantly delayed (up to 12 hours). You can check the "Date:" email header in individual messages to see when they were originally submitted to the SMTP relay.
There is no word yet from SMTP relay's support team on any specifics of the incident.