Chrome win 10 here. I stay logged in to the BAA site if I close the tab but keep the browser open but it logs me out immediately when the browser is closed. Many websites/forums give the choice to be remembered or not (which IMO is the best arrangement) while with others (like Amazon for example and soon Outlook) you have to physically sign out unless you are using private browsing.
British Astronomical Association
Supporting amateur astronomers since 1890