The pilot and pilot-certificated passenger were on a return cross-country flight that originated from Washington, D.C., with a final destination of Lancaster, California. They departed Missouri earlier in the day, and had planned a stop in Colorado. While approaching Colorado's La Junta airport for landing, the aircraft encountered wind shifts, downdrafts and turbulent weather conditions. As the pilot turned onto final approach during one of several unsuccessful landing attempts, the aircraft impacted the ground at an elevation of 4,500 feet msl in dark night conditions.