It wasn't a good situation. Although it still looked like I could beat the onward marching line to Pierre, I had allowed myself to get into a situation in which I had no other option but to proceed to the airport. Then, to add to my concern, Minneapolis Center informed me I would have to hold for other traffic in the queue ahead of me for the approach to the uncontrolled field. Before an airplane could be cleared for the approach, the pilot of the airplane ahead had to report on the ground. I was finally cleared for the GPS to Runway 5. As I descended on the approach and just as I started to get ground contact, the wind strengthened and wrapped around to a tailwind. The airplane began to descend rapidly. I added power to abort the approach and requested vectors for the ILS to Runway 13, the runway the wind was now favoring. But I had to go to the back of the line.