I don't want to diminish the frustration that people feel when they're driven to flounce. The frustrations are usually valid (they've been moderated for reasons they don't understand/don't agree with, they've got complaints or concerns that they don't feel empowered to address in a more direct manner, etc). Unfortunately, that's where the reasonable-ness seems to end, because rather than contact me with a question/concern or simply leave the community, members who are driven to flounce are seeking external validation for their departure.
As a community manager/publisher, my response to flouncing is usually a brief, non-emotional response saying something along the lines of:
I'm sorry you feel this way. I certainly don't expect that this community is going to be a perfect fit for everyone, and I fully support each member finding a space online that feels right for them. You don't need to like all our policies, but you do need to respect them — and if you can't do that, then it makes sense that you'd want to find a community that's a better fit for your needs.
It's basically a very straight-forward acknowledgement that says, "I hear you, but the site isn't changing. I guess this is goodbye."
Some flouncers are actually trolling, in a way — sometimes I feel like I shouldn't respond at all, but I don't like to be accused of ignoring community members. I'm not usually going to acquiesce to most flouncers' requests, but I like members know that their concerns were heard.
It's sad though: sometimes flouncers have legitimate concerns, but when these concerns are presented with drama and a meaningless threat of departure, it makes civil discussion pretty difficult. MAKE THIS CHANGE OR I'M LEAVING puts me in the position of saying, "I'll consider your feedback, but if you need to go, you should probably just go."