Error 0x800CCC0E on clients connecting to a Plesk VPS manifests itself with several descriptions:

Task ‘Checking for new mail in subscribed folders on your_account.com.’ reported error (0x800CCC0E)
Outlook is unable to download folder (null) from IMAP e-mail server for account your_account.com.
Error: Unable to connect to the server. If you continue to receive this message, contact your server administrator or Internet service provider (ISP).

Assuming that there isn’t a problem connecting to the server (in my case mail was being sent and received, but IMAP folders would not synchronise) then the problem lies with Plesk limiting the number of mail client connections from a single IP address – four by default. To raise this limit:

Login to Plesk
Under Server Management, Click “Tools & Settings”
Under Mail, Click “Mail Server Settings”
Change the “Maximum number of connections per IP address” to a larger value, e.g. 40.
Click “OK”