what you describe appears to assume that my network application is web based where HTTP is stateless and "sessions" are created through the application.
Almost. It does, however, assume that sessions are started and stopped relatively quickly (think minutes instead of days).
A TCP connection is established and remains that way until termination.
Interestingly enough, that's how the web works. ;) Either way, you're free to use the methodology that I stated above or not; I won't be hurt if you don't.
The only easy day was yesterday