Can Increased Demand Lead to Decreased Demand?

We're having some guests over for dinner tomorrow night, and cooking fish. So naturally we turned to The Ethical Gourmet for advice on which fish are politically correct. And found this, on skate:

Slow to mature and reproducing in very small numbers, skate are an overlooked problem... The fish are sometimes used to produce fishmeal for aquaculture operations, but growing demand for them from upscale restaurants is also taking its toll.

Let's say that aquaculture operations pick the cheapest fish to use for fishmeal, and that our aim is to kill the smallest number of skate, thereby giving them the opportunity to mature and reproduce. Should we eat skate, or not?

If we do, we're obviously increasing demand for the fish, not to mention eating dead skate ourselves. On the other hand, if we don't eat skate, we're decreasing demand for the fish, which means that the price will go down, which means that skate will become more attractive to aquaculture operations, and potentially even more of them will be killed.

Is it possible that increased demand for skate from restaurants and consumers could bring the price of the fish up to a level where it's no longer economical to use them for fishmeal -- thereby reducing the number of skate killed each year? Is this a case of "multiple equilibria," or something along those lines? Or am I just desperately trying to rationalize the eating of a delicious fish which has long been one of my favorites?