It's a condition called"wet feather," and it can have various causes.
One of my ducks, Lilikoi, sprained her leg once, and it hurt so bad that for days she wouldn't walk on it and could barely stand, holding herself up with her good leg and just bracing her other foot against the floor at an angle. She had no balance, and didn't feel good, so she didn't preen. She didn't preen for a couple weeks. At first, she still got bath time, she enjoyed it and it got her off her leg, but after a while she was no longer waterproof, and water would pour from her when I lifted her from the tub. Getting her dry took longer and longer until I cut off all water access. After she healed, she went through a partial molt and started preening again. It helped, she can have bath and pool time again, but she's still not as waterproof as she used to be. After the annual molt she'll be back to normal.
Having little or no water access can inhibit a duck's instinct and desire to preen, and that could have a similar effect to Lilikoi's injury. An infection of the oil gland or a parasitic infestation on the skin can make preening ineffective, and also cause wet feather.
If I had to guess, I'd say the black duck's condition may have initially started because of an injury, since he/she still has some residual lameness. Either that, or a lack of water at their previous home. Or both. Either way, it'll pass.
You've got a big heart to home these poor ducks. They are possibly the messiest creatures under the sun, but they are such fun and joyous animals. I wish you the best and I hope you form strong bonds with them!
I have to ask, what are their names?
Friend
Spirit
Educator
