I have never seen this problem, but if your first fish has survived it, that is a good sign that there's probably time to treat the other fish.
Can you tell if your fish has a bent spine? If the spine is bending, that might indicate a disease. (Like tuberculosis?)
Also, have you checked your ammonia and nitrite levels in your tank? If these have spiked, it could be that the droopy tail is an early sign of stress and that the fish will return to normal swimming patterns when the water quality has improved.
On the other hand, if your fish were juveniles when you got them and their tails are drooping as they get bigger, perhaps this is a natural deformity?
natural deformity, maybe. I have several danios with gross deformity.
Levels in my tank are immaculate.
Stress, possible, as they have very little swimming room these days due to plant overcrowding. (trying to grow out)
cute - it is.. especially when they swim. Poor guys.
I'm not sure if that other guy is still around. I'll have to peak around. It also causes rapid gill movement. Other fish are not experiencing the same symptoms, but it does seem to be spreading slowly.
I had the exact same thing happen to a Red Danio before. He lived like that for a couple of months slowly deteriorating. He eventually died, but I don't know if it was from the drooping tail or if the other fish in the tank got him in his weakened condition.