This mostly affects calender or addressbook ressources. I start Konact, switch to Calendar and see e.g. that 4 of 5 calender ressources are shown. I can "solve" the problem by restarting Kontact. Has anybody an idea how to figure out what goes wong here?

It has started some time ago and I still see it regularly in the most recent frameworks-based PIM stack.
Qt: 5.7
Frameworks: 5.27
KDEApps: 16.08.2
using openSUSE Tumbleweed.

Do all resources show up in "akonadiconsole"?

Yes, there are all there. I even see all calenders in the Korganizer, but sometimes the events are simply not shown, despite the respective calender is active (inactivate and activate in Korganizer does not help then, only a restart of the App). Analog in addressbook, the respective addressbook is shown on the left, active, but the entries are not shown.

If you can see everything outside of KMail, my guess is that something is awry there. Would you be able to file a bug with detailed information on how to reproduce the issue on bugs.kde.org?

It is there since March this year:
https://bugs.kde.org/show_bug.cgi?id=360030