Get Pet Questions Answered by Pet Experts
Well, I am not an avian vet, but I will give you my opinion.
About 95% of baby duck problems come from environmental or nutritional deficencies.
At this age the duck has no real oils in the feathers so there ability to maintain body heat and stay dry is not like an adult duck. They get chilled pretty easily. The ducklings should have an area in their cage that the temp (via a light source) maintains about 90 degrees. Then enough room to move out of that heat souce to the other end of the cage to eat/drink. It should be eating a starter food with the beginning of pellets being introduced.
Clear nasal discharge (yellow or green implying secondary bacterial issues and the need for a vet) suggest unthriftiness and possibly viral. I recommend separating from the other ducklings and making sure that duck has a warm area to sit in as well as ability to leave it and eat/drink.
Let me know if you need further clarification.