If you've logged in and started a chat session, the website shouldn't expire your sign in. After waiting over an hour, I lost my place in the chat queue. After you sign back in, it should rejoin the chat queue automatically in the same place.
I had one rep who was actually looking into my problem (can’t switch plans) but in the middle of it, the session timed out and disconnected. At the very least they could give you a warning that the chat is going to be disconnected with an option to stay in it.