When akonadi fails to auto-start when kmail starts, I can quit kmail and the window disappears, but the process stays visible in the "System activity" manager until I manually kill it. Using bug #331165 I can easily trigger kmail not starting akonadi and showing the "details..." button on top of everything. When I close the window using the window-manager decoration close button, kmail goes away. Starting kmail again immediately makes it go back to the screen that was there when I quit it. Showing that it never died. Only when I manually kill kmail does it disappear from the task list. Reproducible: Always
I also have the "quits but never dies" symptom with recent KMail/KF5 installed from Git, but I don't know how it is related to auto-start of Akonadi. This is not always reproducible here, but often happens after some minutes/hours of active interaction with KMail, sometimes involving "akonadictl restart" (needed to run it when IMAP hangs up.)