On May 7, 2006, about 0845 mountain standard time, a Cessna 150M, N66705, landed off the runway and collided with terrain at Green Valley, Arizona. The owner was operating the airplane under the provisions of 14 CFR Part 91. The certified flight instructor (CFI), and the student pilot, sustained minor injuries; the airplane sustained substantial damage. The local instructional flight departed Ruby Star Airport, Green Valley, Arizona, about 0700. Visual meteorological conditions prevailed, and no flight plan had been filed. The CFI submitted a written report. They were returning to the airport for a full stop landing. The student pilot had control of the airplane. He turned the base leg of the traffic pattern early and at a high altitude. The CFI assisted the student in losing altitude prior to turning final. The CFI took control of the airplane on final and configured the airplane for landing. He felt that the attitude was good and the landing was assured. He stated that immediately after lowering 30 degrees of flaps a gust of wind caused them to drift off the centerline of the runway. The CFI did not think a safe landing was assured and committed them to a go-around procedure. He executed the go-around by applying full power, enriching the mixture, and turning the carburetor heat off. He waited for the engine rpm to rise and kept his hand on the flap position lever. He waited to bring the flaps to 25 degrees until the lift increased. The CFI said he never got the positive rate of climb that he was waiting for. He never raised the flap lever due to the sink rate of the airplane and their close proximity to the ground. Due to rising terrain and low performance of the airplane, they were never able to execute a climb out. The instructor kept the wings level and pitched for the horizon for best airspeed results. He felt that he was past runway landing possibilities. He banked to the left and impacted a dirt pile before stopping suddenly in the brush. The pilot operating handbook states that during a go-around procedure, the wing flap setting should be reduced to 20 degrees immediately after full power is applied. When the airplane has reached a safe airspeed, the flaps should then be slowly retracted to the full up position. The CFI stated that the airplane and engine had no mechanical failures or malfunctions during the flight.