I was pulled away from this site last month due to some computer issues, so I wasn't able to keep up with you to see how your betta was doing. I had hoped to return and find that his problem was cured, but I guess that didn't happen.
From what I've read I guess that you tried the medications suggested and had no luck. Now I'm beginning to wonder if this might not be due to other factors. If it is not self-inflicted, it may be due to other contaminants in the tank you normally can't test for.
You said that you had road construction going on nearby, did this problem begin around the same time? The construction could be causing water quality issues. This could either be from the tap or from contaminants settling out from the air and into the water. That is only one possibility though. The mini-cycle mentioned before is another, but your numbers look good.
If from the tap, a simple charcoal filter would help, as well as removing the odors and other contaminants from the water. If from something settling out of the air, the tank would need to covered on top to stop it. Charcoal may help with that as well.
Betta's do better than other fish in bowls because they are a still water fish and generally don't like strong currents. Being truly a tropical fish they also enjoy warmer temperatures, like 80-82F, than many fish do. Both of the foregoing is probably why they have adapted to taking in air from the surface to supplement their breathing. I still like to aerate their tanks, but I try to keep it from causing currents by diffusing the air from a larger surface area, say a longer airstone.
It seems to me that this must be related to water quality in some way. If he had a disease that was this resistant to treatment, I would think that your other Betta would be affected as well. That is not necessarily a hard-and-fast rule. Some fish are just more resistant than others.
You might try a journal to keep track of any changes to his health and environment, both inside and outside of the tank. That may help you to notice any patterns that you may have missed before. Keep us posted.