You are correct about the name of the check box. But normally, if you have checked that one, it should prevent that automatic logging out.
Also, on this forum, the "gallery" is the one that requires permissions, attached images do not. Please try the "Basic concepts" thread in "Seamanship" and see whether you can see the images there.
I can see my own gallery images and I'm not logged out.

I can also link to other users' images in my posts.
The issue seems to be that you are being logged out despite asking not to. Do you use particularly aggressive privacy settings that might prevent the site from remembering you?
If you have another browser, or another device, could you try from there? In the meantime, what is your configuration? OS, Browser, etc.
I'll pass anything you find to our webmaster.