Don't know if this applies to to the other decoys, but the HS Strut Snood decoys come with a note stating that they are not designed to be 100% air tight and you are to blow them up and immediately stick them in a hot shower or use a hair dryer on the decoy to re form the shape from being deflated.
I did look at the DS and Avian x and they appeared to be similar material, where the material could actually hold the shape on its own.
Just a thought