so I don't know what's wrong either, but here are some strategies to try to figure it out.
pictures here will help so we can see what you're seeing. feather loss, general condition, oil gland, etc.
separate pen for the ducks and the drake. best if they can see each other so they don't fret (share a fence line) but if the issue is over breeding, and wear and tear on the feathers because of that, you'll start to see some improvement as the feathers grow back in
if the oil gland doesn't look normal, if it's inflamed, might be blocked, and warm compresses may help open it up. haven't had to do this myself so I dont' know specifics, maybe someone else will.
not laying may be seasonal, or it may be not enough protien, or it may be a sign of stress and something going on health wise... hard to know until some other things are eliminated. separating the ducks will let you see how much each is eating. total isolation isn't the plan, because they're used to being in a flock together and will stress, but if you can tell if they're all eating well, or if one is not, that's another clue.
how's their body condition? thin? fat? can you feel their breast bone sticking out or do you have to poke around to find it? too thin, that could be diet or parasites, or other issues, and can cause feather loss or failure to grow, as well as not laying. I've had some fat ducks, and it impares successful breeding, but I don't think it's kept them from laying or making feathers.
how's their crop feel? if you're not sure what's correct for it, feel the crop on the healthy drake and compare it to the ducks... if it seems different, let us know what you notice... might lead to some ideas.
how's the duck's temp? not sure what normal is, but you can check the duck that's doing poorly, compare that to the healthy drake. should be able to find normal temp online.
so time to get out your sherlock hat and see what you can learn...
hopefully some more folks will chime in with more ideas.