Even when that's not the case, the sponsor may have other reasons for not offering a cash option for a trip prize.
There's nothing wrong with politely asking, "Is a cash option offered instead of this trip?" But pushing any harder for cash if the sponsor says no seems ungrateful, and probably won't get you anywhere. It's one of the things I recommend you don't do when you win a prize.
So if you can't take a trip you won, and the sponsor doesn't readily agree to a cash option, simply decline the prize. It's frustrating to turn down a prize you won, but it means that the trip prize will go to someone who can use it well, and maybe you'll improve your luck with the good karma.
Have more questions about winning trips? See my Vacation Prize FAQs for answers to the most commonly-asked questions about vacation wins.