‘Post’ in this sentence suggests place of duty where a soldier is supposed to remain as a guard. If he leaves his post without permission, he will be in big trouble.
You had wondered how I found the correct answer. It was easy as in our country also if a soldier leaves his post he will be punished. As desert (v) means leave (v) the answer went without saying.
I am sorry that my answer to your letter had been few years late, but I didn’t know the rules of the etiquette of the correspondence that also I would have known without saying.