Chronic wet feathers are covered on page 277 of Storey's Guide to Raising Ducks. Dave Holderread says to check for mites, which can cause the problem, or possibly a plugged or infected preening gland. If it is the preening gland, he says to massage it a few times a day, apply a warm compress...
It doesn't look like molting to me. It looks like a preening problem, maybe a clogged preening glad. I remember reading something about treatment in Storey's guide for ducks. Let me go take a look.