I copy a local folder in my imap account.
In my webmail account i see the folder is created and filled with all messages. Good.
I copy another local folder in my imap account.
In my webmail account i see the folder is created and not filled with its messages!
In the two cases the messages are old and tagged as read.
I see that, as far as KMail is concerned, Zimbra supports POP3, as well as IMAP.
Maybe, you could try setting to access the Zimbra account from KMail with POP3 in place of IMAP …
The reason is, POP3 consumes fewer network resources and therefore, the synchronisation may, possibly, be more reliable …