I’ve often found that mail I’ve “sent” hasn’t actually left my computer; I usually don’t notice until much later that the message is stuck in my Outbox. You could argue that the badge on my Outbox is a clear indication that something is wrong, but I’m not in the habit of checking the Outbox. Twenty-plus years of using mail clients that actually send when I hit the Send button has conditioned me to expect behavior that Mavericks Mail somehow doesn’t provide.
This, and other problems with Mail, seem to be universal. It happens to me all the time. I also find that Apple’s Mail repeatedly forgets the credentials I’ve entered for third-party IMAP servers, including GMX, Outlook, Gmail and, even, my own domain, @macfilos.com. This happens also in the iOS version of Mail. I have given up trying to send messages from any of these services via Mail and invariably change the reply sender to @icloud. Even then, as Dr. Drang points out, sent messages often get stuck in the Outbox. And sent messages constantly reappear in Drafts even when they have been sent.
Mail’s facilities are perfectly adequate for me, as they are for Dr.Drang, and I have no desire to move to a third-party application such as Mail Mate. The least we can expect from Mail, as with all Apple’s built-in information-management solutions, is reliability. At the moment, I do not think Mail is fit for purpose.