The pilot reported that during his first attempt to land on the 3,950-foot-long asphalt runway, the airplane touched down too long and he performed a go-around. During the second attempt, the airplane touched down on the first one-third of the runway, when a gust of wind forced the airplane back into the air and it subsequently touched down further down the runway than during the first attempt. The pilot thought a go-around would be too dangerous at that point and applied brakes, but the airplane traveled off the end of the runway and struck and asphalt berm. The pilot further stated that the airplane landed with a headwind of 15 knots, gusting to 25 knots. A witness, who worked at the airport, stated that the airplane was still airborne as it flew over the runway numbers at the departure end of the runway. Examination of the accident site by a Federal Aviation Administration inspector did not reveal any skid marks on the runway; however, the inspector observed skid marks in the grass beyond the runway. The inspector did not observe any preimpact mechanical malfunctions with the airplane, nor did the pilot report any. The inspector added that during the impact, the airplane sustained damage to the firewall and lower fuselage.