The private pilot undergoing instruction (PUI) was undertaking a mountain checkout in order to rent the airplane. The certified flight instructor (CFI) and PUI obtained a full weather briefing and the CFI had been to the airport on many occasions. They listened to the weather observation taken from a nearby mountain pass and the winds were reported from 090 degrees at 8 knots. They over flew the airport and noted that the windsock was indicating calm winds and they elected to land to the south. During the approach into the mountain airport, the CFI noted a light bump over the approach end of the 2,875-foot long, 30-foot wide runway. After calculating takeoff distances and determining density altitude, the CFI and PUI noted that the windsock was still indicating calm wind conditions, so they elected to depart to the north (the calm wind preferred departure route). The CFI noted that the temperature was 18 degrees Celsius. They configured the airplane for a short field takeoff, applying 15 degrees of flaps. While holding the brakes, the PUI added full power and began the takeoff roll. The CFI noted that maximum static power was being obtained. The PUI rotated the airplane at 50 knots (target speed was 56 knots). Approximately 15-20 feet above ground level, a gust of wind blew the airplane to the right and the CFI assumed control of the airplane. The airplane then sank. At this point, the CFI elected to discontinue the takeoff and as the airplane settled downward, he noted a newly installed guardrail at the end of the runway. He applied additional power to overfly the guardrail and land in a clear area beyond it. The airplane began to slow and then impacted a ditch and nosed-over.