Because I cannot use my laptop when this happens, I'm not sure _what_ kmail is doing -- either downloading mail, or filtering it. When it happens, I can switch between applications, but those applications (like firefox or akregator) cannot redraw. Only konsole seems able to get user input. I am pretty sure it _is_ kmail, because it only happens when kmail is running. Reproducible: Always
This bug has only been reported for versions before 4.14, which have been unsupported for at least two years now. Can anyone tell if this bug still present? If noone confirms this bug for a Framework-based version of kmail2 (version 5.0 or later, as part of KDE Applications 15.12 or later), it gets closed in about three months.
Just as announced in my last comment, I close this bug. If you encounter it again in a recent version (at least 5.0 aka 15.08), please open a new one unless it already exists. Thank you for all your input.