The server is limiting how much your client is doing at once.
WHAT CAUSES IT
A mail client opening many simultaneous connections, which some clients do when synchronising large mailboxes Several devices synchronising the same mailbox at once A client configured to check every minute An enormous mailbox being indexed for the first time
WHAT TO DO
Reduce the check frequency to every fifteen minutes Reduce the number of simultaneous connections in the client's advanced IMAP settings, where offered Wait for an initial sync to finish before adding more devices Reduce the number of subscribed folders if you have very many
IF IT PERSISTS
A mailbox with tens of thousands of messages in one folder strains every client. Archive old mail into yearly folders, or to your computer, so no single folder is vast.
ON SENDING
A similar message when sending usually means the hourly sending limit rather than connections. Sending pauses until the hour turns over. If you are hitting it without sending campaigns, suspect a compromise and open a ticket.