Our email provider suffered a major hardware failure, which they have since recovered from. Email is sending successfully again, though they have warned there could still be periods of intermittent availability as they stabilize their API.
Email API Outage
The intermittent availability issues have been tracked down to timeouts due to our email provider's API being offline. We have taken measures to prevent the API timeouts from causing performance issues on sites. However, emails may not be going out from sites. We are working with our email provider for a resolution.