Here only the wooden chair is pickable, but even if all meshes are pickable, the issue still persist without any apparent pattern - just from time to time.
I had this once. I made a extra null check in the routine. It had to do with clicking through the open areas and resulted in no mesh. Maybe this will stabilize it and makes debugging easier.
Thanks for the suggestion, I did this already but with no effect.
The room is closed. Anyway, it happens even when I am moving pointer over the floor only.