Well, you might be dealing with 2 things at once, a) the getting stuck in the bucket deal, and b) a possible molt, 4 mos seems about right. I just noticed my #4 duck losing feathers and beginning her molt today.
The best thing to do is make sure she is consistent access to a clean swimming pool and ample time to preen. You could address this issue from the inside by adding some vitamins, maybe a *slightly* higher %protein feed for a very short time, but those things certainly shouldn't be necessary. A good healthy splash of Apple Cider Vinegar would be good to add to the water too.
