It’s happening to me as well. I can recreate it every time by just closing the browser (Chrome, Windows) and loading up my Ottoneu bookmark (which is the league home page).
There is certainly a thing the baseball site does if you visit a page in your league, then log in, it will give a message saying that you must be logged in even though you are logged in. That’s been true, unfortunately, since … probably 2013.
However I am not seeing any situation where Ottoneu baseball is not logging people in, similar to what the original issue was with football. My first click to my league home page from the user dashboard looks exactly as I’d expect it to.