Jim, I hadn't realized you were loosing fish - multiple fish. I sure am sorry about that. I share your pain, as I have the one with dropsy who I know will die soon (haven't seen him in two days). And yesterday, there was one dead, one who had been "perfectly healthy" the day before, and just popped up dead, not a mark on him. A beautiful bright white fish with bold black and orange spots. I got him to replace another uniquely bold white fish, who also up and died for no apparent reason, about a year ago.
Your Blue was gorgeous, especially with that line of horizontal scales along his sides.
But I'm not convinced the problem is dropsy. Yes, in some of your posted pics the fish look fat, most notably pushing out from the bottom (but that's hard to tell from the pics). But just being fat is not necessarily dropsy. In dropsy, as I understand, the fish puffs out from the sides, and it always includes protrusion of the scales, like a pine cone, as the fluid builds up inside the fish and the body swells. Also, dropsy is not contagious, so it would be highly unusual for several fish to contract it at the same time.
Either way, SOMEthing is killing your fish, and you've got to do something. Just need to figure out what it is.
In my research on dropsy, it's bacteria that attack the kidneys that causes the malady. That bacteria has to live somewhere, and I'm guessing it's in the water. Now, above, there was the mention of "strirring up bacteria" by messing around with the water, and that makes sense. But it also makes sense to me that, if the bacteria is swimming around in the water (and there may be even more, if you have dead fish polluting the water), that a partial water change, or even removing the fish to a whole new, clean tank, would reduce the exposure to bacteria.
Remember, this is coming from someone in Houston, the almost-tropical Gulf Coast, where winters are moderate, and, for example, today's temp is 74*
And yes, any of that is going to stress an already stressed fish.
It's a quandry. I really don't the answer. Either let nature take its course and hope for the best, or take action, whether it's the right acvtion or not. I didn't find a lot of KoiVet, other than injections of an antibacterial medication that I don't have access to, nor any way of administering (and that's even assuming I could catch the fish in the first place!), and, from everything I've read, once they puff up, it's too late anyway.
On my thread about "OMG - Dropsy" in the Pond Chat forum, I believe I posted a suggestion I got from the expert in our (Houston) Lone Star Koi Club. He suggested salting the water, to help draw excess moisture out of the fish, along with injections and warmer temps. Go look up that post for correct details.
Good luck. Man, it's bad enough loosing a loved fish; I sure would be sick if multiples of my fish were dying. Sorry.