Timeshare Problems

My father passed away last December and he named me as Executor of his Will. We live in Georgia. He owned a Timeshare property which was in his name only. The Timeshare property is located in South Carolina. This property was completey paid off and of course, he had been paying the yearly maintenance fees. I notified the Timeshare Association of my father's death and let them know that no one in the family was interested in taking over this property. They wrote me back and tried to get me or someone in the family to take over the ownership. I again wrote them and informed them that nobody in the family was interested. They have been calling my house every week and asking if my father was there; I have told them repeatedly that he is deceased and to please quit calling me. This past week I received a letter from the Timeshare Association Legal Department informing me that the S.C. law requires that upon the death of the owner, probate must be filed and a deed of distribution must be filed in the county where the property is located. They state that I must become the owner of the property to legally convey the property back to the association. If I become the owner there is no guarantee that the Association will take the property back.
As the Executor am I responsible for taking over the yearly dues for this property? What happens if I do nothing? I can't afford to pay these yearly dues for the rest of my life, what are my options. I need help!!