I am a windows user and I have suffered from the same problem as you: if you take too long to compose your reply, the system logs you out, and therefore does not allow you to post it. I am virtually certain that this system behaviour is justified on the basis of what the site can afford to spend on bandwidth.
Here's my workaround. When you get the "you are not logged in" message, cut the entire text of your response. Then open a new tab or window and restart usingenglish.com and log in. Return to the thread you were trying to respond to, click reply, and paste, then post.