If there is a connection problem with the IMAP server (maybe the same with POP3) then KMail switches the respective account to offline mode. But there is no obvious hint for this change. You have to click on the folders belonging to this account to notice the change. This can be quite annoying if there are many accounts and the affected one is not important. I often miss mails for several days because I am not aware that a certain mailbox (with low traffic and usually not so important messages) is offline. The solution is obvious and very easy to implement: If an account is switched to offline then KMail should automatically try to reconnect after a reasonable time, say every hour. An alternative or parallel reaction (very easy to implement, too) would be to add an optical hint e.g. change the folder icon to red or add a new element above the folder list. Reproducible: Always
I forgot to mention that there is a similar bug entry: https://bugs.kde.org/show_bug.cgi?id=332652 But the described behaviour is not a bug IMHO. And the proposed solution seems a bit simple.
I am experiencing this error with KMail 5.3.0. nd in prior versions. When I login, I have a cryptographic key setup to unlock kwallet, which means there is a delay in the credentials for signing onto the available networks. This delay means autoconnect usually fails unless I unlock my wallet fast enough. The failure to connect stops KMail from retrieving new messages. After connecting, KMail fails to detect the change in the network status, and will remain so until I manually restart the IMAP connection. Prior to noticing this issue, I went for days without receiving or responding to emails, simply because I was trying to connect to networks requiring authentication.