The login screen has a check box for 'Remember Me'.
I have the box checked, but if my session expires then the client logs me out and I have to enter my username and password again. (Seems to happen after watching a couple of long replays one after the other, but watching replays is all I've really been doing so far).
Also, after the session expires, the area where you type in your login and password will be missing (normally located at the red question mark), but the area where you choose the server is still at the bottom of the screen.
The only way to log back in is to restart the client.