I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site and even less who are familiar with waterfowl. There are a number of common diseases of ducks that affect young ducklings...
Duck Virus Hepatitis - if spasmodic contractions of Peanut's legs arise death is sure to follow within an hour in a typical "arched-backward" position.
Duck Plague (herpesvirus) - usually seen in mature ducks but also in ducklings - if greenish-yellowish diarrhea (sometime blood -stained) arises you'll lose this duckling.
Riemerella anatipestifer - listlessness, eye discharge, diarrhea, incoordination, shaking of the head and twisted neck are seen; birds are commonly found on their backs paddling their legs.
Avian cholera - loss of appetite, mucous discharge from the mouth, diarrhea are ssen
Colibacillosis - symptoms are similar to Riemerella
Toxins - botulism - progressive flaccid limp paralysis of the neck, legs, and wings; birds usually die in a coma within 24-48 hours; this would appear to be an important differential diagnosis for Peanut
I wish I could be more specific for you from here. Supportive care would involve force-feeding a gruel of duck pellets and keeping Peanut warmed in an 85F environment. Unfortunately, his prognosis is grave. Please respond with further questions or concerns if you wish.