Similar things happen to me if I leave my computer for say 10 minutes and then after I click on a thread or forum to read, the page will open but it shows me as not logged in so I don't think it's a "remember me" issue but rather being logged out on the back end due to inactivity-and that's what I think happened to the OP as all he/she was doing was typing into a message oust box and the website doesn't think that is "activity".

Now as to possibly losing a long post or pm because of this, what I do is periodically preview my post/message as that is activity as far as the website is concerned and that keeps me logged in. Also, right before hitting send/post, I copy the entire body of my message/post

But going back to the beginning, I don't think this is a remember me/keep me logged on but more of the system/website timing me out due to inactivity