My Mac Mail does not automatically download mail even though preferences are set to download mail every 5 minutes. I have to click on "synchronize mail" each time to receive mail. My main email address is an IMAP account.
From the Mail menu bar, select
Mail ▹ Preferences ▹ Accounts ▹ Advanced
and check the box marked
Include when automatically checking for new messages
Repeat for each account.
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