php and flash chat program

Hey, I need some advice if anyone is willing to offer it. I have a chat program I am working on. The interface is built in flash, and it uses PHP also. There is a main chat area where the users type their messages back and forth, and there is also a smaller area which displays all of the currently logged-in users. When a user logs into the chat room, it adds their nickname to a users.txt file, which creates a list of all the online users and is then displayed in the chat page. I also have a logoff button that will search for the users nickname in the users.txt file and remove it, so that it won't be displayed in the chat window anymore. The only problem I am having is that if a user doesn't click on the logoff button and instead just closes the internet window or shuts off their computer, then their nickname will still appear in the list of users, since it wouldn't get a chance to be removed by the logoff button. I'm not sure how to accomplish this, I would appreciate any help you can offer me. Thanks a lot. Matt