It's a plant. Think of it as a cut flower. After cutting open a pumpkin, they are obviously no longer sealed. They start to dry out. You can rub petroleum jelly all over the carved sides to help slow down the drying out. You can also soak them in the tub, and they will pull in some of the water to help them come back into shape.

There's all sort of things you can do to prolong things once they've been cut/carved/etc. My mom was a florist and designer. I've been in/around productions requiring things to be preserved so items can be kept around as long as possible. You just kind of pick up a thing or two