I'm very sorry to hear about your duck.
I would trust your vet, if they say he has an infection. They likely listened to his chest with a stethoscope and could hear abnormal respiratory sounds indicative of a respiratory infection. Maybe they did radiographs, or bloodwork. Duck's bodies are very good at "walling off" infections, but that makes it so that systemic antibiotics aren't as effective as we would like for treating the infections.
In my experience inhaled medications work a lot better for respiratory infections in birds. It is unfortunate that the vet you used doesn't treat ducks anymore. Can you find another avian vet? With my birds once they stop eating they are in critical condition and need tube feeding and immediate medical care.
Also, it isn't unheard of for medications to work and then stop working with respiratory infections. That happened with my duck as well. Then we switched to inhaled, and that worked for a while and then stopped working, too. Respiratory infections in birds can be very complicated and even require surgery, depending on what you are dealing with.
Of course, I don't know what you are dealing with - so I recommend you take him to another vet. He will have the best chance of survival that way.