I found this article for you.
There is a work around proposed b Apple but no permanent fix.
Apple posts workaround for Mavericks Mail sync issues, no permanent
by NDTV Correspondent, February 04, 2014
There's good news and bad news for users of Apple's Mail app who have
been plagued by problems since updating to OS X Mavericks. Apple has
acknowledged that users are still having trouble despite multiple
updates since a new version of Mail first released with the updated
operating system, but the suggested fix is only a temporary
Apple suggests that users disconnect and reconnect from their mail
servers by selecting 'Take All Accounts Offline' and then clicking
'Get All New Mail' from the Mailbox menu. This has the same effect as
quitting and restarting the app, which is what many users had resorted
to doing. Apple also helpfully adds that these two commands can be
added to Mail's main toolbar by clicking 'View > Customize Toolbar'
and then dragging them from the palette that pops up to the desired
The workaround does not fix the underlying problem, although Apple's
acknowledgment means they know it exists and are hopefully working on
Since the release of Mavericks, also known as OS X v10.9, users have
complained that the Mail app refuses to download new emails and that
they have trouble while moving and deleting messages, especially when
connected to Gmail accounts. Such problems relate to the desktop
software's inability to synchronise changes with remote mail servers.
Two previous updates, including a dedicated Mail Update and the
overall Mavericks 10.9.1 release failed to fix these problems for many
users. Apple's release notes for 10.9.1 specifically mention improved
support for Gmail, reliability fixes, and improved search and mailbox
Other problems relate to mail being delivered late, folders and tags
not updating, and searches not displaying messages that are known to
What I read from it, is Apple knows about the IMAP issues and it is working to fix it. So far the 10.9.2 has not completely resolved it.
I suggest you open the Activity window in Mail to monitor the progress if you have multiple accounts (it might take a while), before doing the get mail (go online)