C172 flight instructor reported an engine failure on a touch and go maneuver resulted in land to a rolling stop.

Narrative

Performed a training flight in the vicinity of ZZZ. After touching down at ZZZ with the intention of doing a touch-and-go on Runway X; added full power in order to continue the touch-and-go and the engine did not produce any power rather proceeded to stop. During our descent we 'cleared' the engine several times by adding almost full power to ensure the engine was still working. The airplane was producing power until about 100-200 feet AGL. The engine gauges were frequently checked through the flight with the last check being done at 1000 feet AGL and no defects or abnormalities were detected. After realizing that the engine is not responding to the advance in power we proceeded to let the airplane roll forward and took an exit taxiway off the runway and pulled the plane into a safe parking space. The plane departed on this flight with full fuel and adequate oil levels after a full pre-flight check; at the end of the flight the airplane still had plenty of fuel and adequate oil but could not be started. No other problems or defects were noticed.