There's no way to get a "draw" on him. I have no evidence at all, but I think that he might kill ANY attacker, even the highest leveled Neopets, even when he only has 200 HP or so, and will only lose to whoever gets the very last hit on him (regardless of BD level). I really don't know, though.

The first one started with at least 10K HP I believe, and was impossible to beat too, so don't worry which mayor you're fighting; the odds of you winning are STILL practically zero.