At the point where you begin to mind it personally. This, like everything else, is entirely subjective.
Angry Birds? Candy? T-shirts at the Target? In my eyes, whored out to hell and back, quit it, I'm so sick of it.
Persona 4? With its anime, rerelease, stage play, fighting game, light novel and manga spinoff? Awesome, you deserve it Atlus. Do it more.
Why? No reason other than I liked Persona 4 more than I did Angry Birds and do not mind seeing it everywhere. I think everyone has one of these franchises that they cannot get enough of, so there's really not an objective standard of measurement for what constitutes "whoring out" or "milking" or whatever.