I seem to recall having read that this is a known Mavericks bug.
Possible solution: seem to recall reading that if you use your @icloud or @me account, that has fixed the issue for some people. Other mail services are not working.
And, as other's have said, computer needs to be on and not asleep. And I seem to recall need to be using Mac's Mail app, no third party-readers (Calendar gets the e-mail settings for an account from Mail).