From being in the same position and trying to "get off the ride", I can tell you that it's a coin flip for success while constantly arguing them is more like rolling a 20.
95% of the time when someone is being a bully, they are doing it because it is giving them attention. They b!tch, people respond. And that's the problem - when *you* start to ignore them, that doesn't mean the rest of the message board will. All it takes is one response for the bully to see that his words have taken affect.
The best solution I have found is, after you realize that they ARE being a bully and not just being overly harsh on their critique, is to ban their IP. Yes, it sounds big brother-ish, but it works. Sure, the bully can find ways around this, and then you ban him again. Lather, rinse, repeat until he gets tired and moves on to b!tch on something else.
In the meantime, you've saved time (how much easier is it to ban an IP than to put a rational paragraph together for someone who won't listen?) and kept a flame war off of your boards (he's spending his energy to get back to the boards, not to fight your words). It's not a utopian answer, but it's the best that I've found.
The decision doesn't have to be logical; it was unanimous.