It’s funny, but my system now works the opposite. I used to have to login each day, and as soon as my browser (not the individual tabs) was closed, next time one, I’d have to login again. Now it stays logged in.
I am guessing the site uses a cookie to save login info. If your browser is set to clear the cache when shut down, then I think you would have to login each day as I used to do. I did not explicitly (or perhaps I should say intentionally) change those settings, so I am not sure what happened with mine.