Hi,
Well, I am not able to reproduce the issue myself, so I cannot give you any updates. From my tests and point of view, clid privacy works as expected even after reloads. If someone can give me access to a system with such behavior I would be able to take a look.
Just to be clear, privacy=clid in a button will make the callerid or dialed number to be omitted in that button, nothing else, nothing more. Maybe you are experience some other issue?
In my tests I set my own panel with privacy on some buttons, and it worked fine for several days...