On December 13, 2020, about 1250 Pacific standard time, a Cessna 172, N5098E, was substantially damaged when it was involved in an accident near San Diego, California. The flight instructor and student were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight instructor reported that the purpose of the flight was for the student pilot to practice touch-and-go landings. During the second takeoff on runway 28R, as the airplane was about 100-150 ft above ground level, the flight instructor detected a loss of engine power and assumed control of the airplane. He landed the airplane on the remaining runway; however, the airplane overran the departure end of the runway and struck and airport perimeter fence. Postaccident examination of the airplane by a Federal Aviation Administration inspector revealed that both wings and the fuselage sustained substantial damage. Subsequent examination of the airplane’s engine revealed that the No. 3 cylinder’s intake shroud tube was bent. Removal of the No. 3 cylinder’s rocker box cover identified the exhaust valve rocker arm stud had separated. The exhaust valve rocker arm seat, rocker arm, washer, and a section of the stud with self-locking nut were loose within the rocker box cover. Fretting was observed at the mating surface for the rocker arm seat, the rocker arm seat, the shroud tube and the push rod assembly. The rocker arm stud was sent to National Transportation Safety Board Materials Laboratory, Washington, DC, for examination. The examination of the fracture surface revealed characteristics consistent with a fatigue fracture. Review of maintenance records did not reveal if the stud was ever replaced or inspected during the major overhaul.