After you've messaged someone, don't click the window closed. If you click the window closed it signals to the person at the other end that you are off line. Just send the window behind the home page by clicking anywhere on the home page (other than an active link) and then the lines of communication remain open.

The downside to this is that you'll end up with several open windows on your desktop and I don't think I can cure that because it's just the way the system was designed.