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I have the option checked, but since some days ago I need to put my user and password every time I restart the computer. I'm on Windows 10.
I read somewhere that some people experienced Settings that don't stay,
someone mentioned that the GOG Galaxy Game Library is not keeping
their Library Categorized the way they wanted to set it up.

So maybe the User Problem your experiencing is related to this problem.

I don't auto Sign-In so I always put my Password in,
so I don't know what to say here.

I'm not experiencing this, though.