I had the chat windows stay up once yesterday, but couldn't reproduce that after I restarted (did manage to hotkey build a war factory with the chat window up). I just started the game again and the chat windows stayed up, with WASD moving the screen and being input into the text box. After hitting Ctrl-Enter, typing some text and hitting Enter again, though, the chat window closed (couldn't reproduce the problem to see if hitting Ctrt-Enter actually helped or that was unrelated).
