preview privileges?

After transition to Sierra Preview.app lets me look at about 100 pictures and/or pdf:s. After that preview tells me I'm not authorised to open them any more. I don't believe there is anything wrong with the pics/pdf:s themselves, as Skim and Graphic Converter still can open them. After restart it's the same procedure: ≈ 100 pics are ok, then it stops.

Privileges on pictures are set to RW for me, Read Only for staff and everyone. I can change them, but it doesn't make any difference - I still can't open them.

On Preview.app the privileges are Everyone: adjusted (?, my translation), System: RW, Wheel: Read only, Everyone: read only. I can't change any of that, I'm not permitted.

Btw: there is a small lock on Preview.app. I don't know if it's always been there.

Any hints what I can do about it?