To date, I have had the same problems. When I reopen the 'site after some time, I have to log in again and then it tells me "you are already logged in". So then I stay logged in for some hours. Even if I visit other sites in a session and then come back to the Reg I am still logged in, for a while. Other forums don't seem to have the same problem, if I save the 'open' page as a bookmark. It is a small problem on a site that is extremely helpful and knowledgeable. I have arrived the 'remember me' and also have auto password set on my computer.
Maybe I missed it but was this ever fixed? I still have to log in every day, unlike other forums where I can save the auto log in details. Maybe I am doing something wrong, but I have Bookmarked the main page and 'remembered' me.
It still doesn't work for me - the "Remember Me" just saves my details, it does nothing to keep me logged in.
On other forums I post to regularly, there is a check box for "Stay Logged In" (or some such instruction) - some allow me to remain logged in for eternity, others have a drop-down box that lets you decide a time limit or "Never Log Out".
For the record, I'm on a Mac, my OSX is El Capitan (10.11.6) and I'm using the latest version of Safari (10.1.2).