1. Open kmail and go to your inbox. In my case online imap. 2. Click on some emails and press R to open a reply composer window. 3. Close the main kmail window via the X in the window title. The composers will stay opened. 4. Start kmail. In my case middle-click on the kmail icon tasks icon. It's main window re-appears. 5. Send an email via some webmail interface to the imap account 6. Click on "retrieve email" in kmail. The account is not shown as offline but the email does not appear in the message list. 7. Close the open composer windows and kmail and restart kmail. The mail does now appear. You can do this over days. As long as the composer windows stay open and just the main window is restarted no new email will show-up in the inbox. Reproducible: Always
The number of new emails shown in blue next to the folders does seem to increase though. It's just the message list which does not get updated.
Fixed in 09fb48c3fa92ccb81409d2f5641190f76433b29c