There is a misconception that the hornet's nest is supposed to hold air like a balloon. This is not the case. The nest is made out of a foam that should hold its shape once it has been inflated. It make take several attempts before the nest begins to hold its shape. Here are a few suggestions to try if you are having trouble.
1. Deflate the nest completely. Then roll it up tightly starting at the bottom. Repeat that several times, rolling it in the opposite side each time. That should help relax the creases. Inflate it again.
2. Use light heat from a hair dryer and reshape. Warm water may work also.
3. Put your finger over the small vent hole at the bottom and forcefully blow into the larger hole until there is pressure inside the nest. Release the air and repeat several time. This will help stretch and reshape the foam.