OS X Mail Stops Syncing Messages
Mail in OS X may stop syncing messages for cloud-based accounts such as IMAP or Exchange Active Sync (EAS), eg Office 365 or Outlook Anywhere.
This may occur when there are a large number of messages.
To resolve, close Mail by pressing Command-Q (⌘-Q) or choose Mail → Quit.
Then re-open Mail. Let it resync, which may take only a few moments, several minutes or longer depending on the amount of work to be done.