Because your browser seems to be clearing your cookies which is how steemit and many interfaces store these settings. They don't store them on account level. Steemit stores it in this cookie. 
I say because but hey tech is weird it could be any shit. I also turned on braves cookie blocker for 3rd party content that does not seem to block it and as you see , the expiry is a month which means it will clear itself. Without knowing your browser etc I can't really say why yours is constantly cleared and to be specific clearing cache won't clear cookies unless you check all those options. but a general f5 hard reload and clear cache should only clear image and script downloads. You can try setting the preferences in settings as opposed to from the posting window and see if that persist better although both perform the same action and sets the cookie in your browser.
I suspect you are right. I had assumed that such a setting would be at the account level; it really doesn't make sense to me to store it in a cookie. I use Brave in private mode pretty much all the time, and clear all cache/cookies on exit. So I probably should have thought of the cookie option. Thanks for taming my rage against Steemit :)
Incognito > private mode, since it chromium which is just chrome does not store session data. Incognito anyway has access to stored passwords so no real reason to use it except for history tracking and seeing as you can by default block adverts and cookies I don't see a use for it apart from porn.
I don't follow, isn't private mode brave's version of incognito?
yeah... was my arrow not clear enough? :)
I guess not. Or, I might just be stupid today.