I used the email-ext to set up notifications for build success, but had Jenkins set up to use an smtp server that was company-internal. This worked fine when I only had company internal mail recipients, but when I added an outside recipient, the build failed because email-ext returned an SMTPException: Could not deliver. All this is fine and expected in a PEBKAC situation.
However, when I had set up a new, proper smtp server in Jenkins and sent successful test emails through the Jenkins configuration page, I figured everything would be fine. But the next time a build finished, no emails were sent out even though the build finished as normal. Checking the logs I found that it said:
Email was triggered for: Success
Sending email for trigger: Success
The two usual last lines with "Sending email to: blah@blah, Finished: SUCCESS" were missing. Obviously email-ext was unable to recover from the previous error even though the settings had been corrected. I worked around the problem by restarting Jenkins, and everything started working as expected with the new configuration.