All 17 Email Delivery sections
When a message is refused
Mail servers get busy. Rate limits bite. A network blip closes a connection half way through. WordPress treats every one of those exactly as it treats a wrong password: wp_mail() returns false and the message is gone.
With Keep a refused message and try again on, it is kept instead and sent again after ten minutes, then twenty, then forty, up to the number of attempts you set. Then it is marked as given up on, which is visible, rather than disappearing. An attempt cut off part way, by a host that stops a slow request, is not tried again, because the message may already have gone: the daily tidy-up marks it as given up on once it is a day old. Until then, Send again on the message's page is there if the customer says it never arrived. After that it is there only if you keep messages, because the copy kept for the retry is deleted when the message is given up on.
Switch it off and nothing more is tried. Messages still waiting are given up on at the next daily tidy-up, without another alert: each was reported when it was first refused.
You can also press Send again on the row yourself (see Sending a message again, above), or send every waiting message at once from the command line with wp email-delivery retry, which does not wait for each one's next try to come round. On a copy of the site, where email is held (see Copies of your site), nothing in the queue is tried, and the command sends nothing.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.