How do you stop EM Client trying to sync a particular account..that may be now dormant but not deleted?

How do you specify that only certain accounts should be synced?

Unfortunately with IMAP and Exchange you can’t do that as all those protocols do is provide a cached copy of what is on the server. If you remove the protocol, you will remove the messages from eM Client.

If you want to keep the messages for reference, you can move or copy them to Local Folders, then remove the account from eM Client.