Still digging for sources, but this is a summary of what I remember:
Here are two places that say it:
http://modernfarmer.com/2014/02/fascinating-nature-duck-sex/
http://scribol.com/environment/animals-environment/the-disturbing-mating-habits-of-ducks/
Now, here's the study they were talking about, and when you actually read through it, you will notice there is no mention whatsoever of ducks losing their penises each year. One article added that in for whatever reason, and then I'm thinking the author of the second article that doesn't mention the study read it in the first article, didn't fact check, stated it as fact in their article, and thus the spread of misinformation was born.
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0000418
The study was done on muscovies, and you raise them. So do you find muscovy penises all over in the Fall? I'm thinking not
