Too stale, too quickly. What do I do with a recipe that is predominantly cornstarch?

I have a delicious donut recipe that is predominantly starch. It turns out great right out of the fryer and for maybe an hour after that, but then it becomes horribly stale. The inside is quite dense, like a cake donut. When it becomes stale, it's just as bad as a denser white bread that has been left on the counter for a week. I suspect that the main problem is the huge amount of cornstarch, but that's something that I can't change, because of the way I need the donut. Is there any remedy to this problem? Thank you!