Prior to takeoff from the 6469 ft MSL airport, the pilot leaned the mixture at 2000 RPM. Density altitude was approximately 9100 ft MSL. The 10-degree flap takeoff and climbout to 300 ft AGL was said to be normal initially; then the aircraft began losing altitude although the engine RPM remained at about 2000 RPM. The pilot said he raised the flaps and lowered the nose to reacquire VY, but the aircraft continued losing altitude. The pilot decided to make a precautionary landing in open pasture approximately 3 miles west of the airport. The pilot reduced power and deployed full flaps. The aircraft touched down and, during rollout, hit a small gully and flipped over. The pilot said heavy rain fell 45 minutes after the accident. According to Gallup FSS, a thunderstorm moved south of the airport at 1349 with rainshowers of unknown intensity in all quadrants. Aircraft handbook states that the mixture should be leaned at full power.