I don't know if this is a Kmail or an Akonadi issue, but every day, when I launch Kmail, it retrieves my emails fine, but then after an undetermined amount of time (a few minutes, maybe more), it just stops doing so. Typing "Akonadictl stop" and "akonadictl start" in a terminal solves the problem, but I have to do it 20 times a day, it's really getting annoying. The thing is, I have no mean to tell WHEN Kmail decides to stop retrieving emails, because it continues displaying old emails fine ; I just have to guess that it "crashed" when after an hour or two I get no email at all at work. i'm using Kmail 5.6.3 on up-to-date Arch Linux.
Could you confirm your mail configuration (how many accounts, whether POP3 or IMAP). Also what is the state of the fetch progress bar (to the right of the status bar) when KMail stops working: i.e. not shown, at 0%, at 100% etc.
I have 2 IMAP email accounts, one with many folders and filters. The fetch bar is not shown when Kmail stops working. Hitting F5 on a folder does nothing at all.
I don't know if that will be of any help, but sending email works fine even when the retrieving bug occurs.
I'm running KMail version 5.6.3, Arch Linux with Qt 5.9.3, KDE Frameworks 5.40.0 and Plasma 5.11.4. I use two IMAP accounts (Gmail and Outlook) and here is happening the same problem related by tromzy@free.fr At the same time Kmail stops retrieving e-mails, it works for sending e-mails.
This morning I noticed that the bug occured while the fetch progress bar was stuck at 100% on synchronizing an IMAP folder. May be a clue.
Another thing I noticed : Kmail keeps retrieving emails in the other account I have in which I did not create any folder. I think the problem lies in the folders.
This bug has stopped happening for a while now.