tmbt
Sounds like an IMAP problem to me, & how the email client responds or behaves when using the IMAP protocol.
It could also be affected by the access time where there is "slowness" on the LAN between the client & the IMAP server.
Also do you have lots of messages in the receiving Inboxes, ideally you would keep the Inboxes empty & move messages to other archive folders.
Tell your clients to use the Refresh or Resubscribe function periodically.
Thunderbird is usually well behaved, do you notice the problem there, or moreso do you notice the problem in Outlook ?