Codewalker: based on the fact that at least one, perhaps many players have stumbled onto this problem, I would recommend that when the close window button is clicked on Paragon Chat, a warning is displayed telling the player that if they close the window, Paragon Chat will close down and City of Heroes/Paragon Chat will not work properly after that point. They should do that only if they have already closed Cityofheroes.exe (in fact, maybe PC could check to see if the child process is dead and if not then display the warning, and close quietly if Cityofheroes.exe is not running).
I have added this to my Common Questions and Problems thread, but you might consider adding this warning to your FAQ first post as well.