I send a gentle reminder just to my immediate point of contact to start. If that doesn't work, I start sending more business-like requests for payment every week, and I CC anyone I think might help make it happen.
I've never fired anyone, and everyone has eventually paid (knock wood), but there have been times when I assumed the money was a lost cause (though never five figures worth like the person who shared this blog post).
But more than once, I've had a client contact me and request new work, and I've had to remind them they still have an unpaid invoice. I'll tell them I can't start anything new until the old work is paid. They almost invariably blame the delay on their billing department, and the money eventually finds its way to me.
Well run businesses will pay you on the 29th day. :)