I don't use the stay logged in option, but I get 2 variants of this bug (increasingly) as the session is 'ended too early'
Sometimes, when I try to log in again, the saved logging information at the page is available and I'm able to relog instantly, but at least in these cases I can see my name among online members (before relogging)
The other variant is, that the saved logging information is not available, when trying to relog in the same browser-tab, I have to close the tab and open a new one, this normally will work.
Edit: Just adding a screenshot here: