The student pilot stated that he was performing touch and go landings prior to the accident. Shortly after his third landing, the airplane veered left and impacted a taxiway sign. The nose landing gear separated from the airframe and resulted in substantial damage to the firewall. Examination of the airplane by a Federal Aviation Administration (FAA) inspector revealed that the upper scissor bolt, cotter pin, and castle nut were missing. Winding tire marks were observed on the runway prior to the airplane veering off the runway. Examination of the airplane by an airframe and power plant (A&P) mechanic found no damage to the nose landing gear scissor flange, or nose landing gear scissor. In addition, the upper scissor flange bolt was not recovered, nor was any evidence identified that indicated the bolt was in place at the time of separation. An annual inspection was performed 17 days prior to the accident flight. A visual examination of the nose landing gear was performed, but no maintenance was required to be performed. The airplane accumulated 18 hours of flight time after the annual inspection prior to the accident.