C172 Flight Instructor reported the engine failed temporally during a training flight.

Narrative

My student and I were in the practice area at 3000 feet approximately 10 miles northwest of ZZZ conducting our Commercial Phase 1 Dual Night maneuver lesson. The controls were transferred to me to introduce and demonstrate a power off stall (full) and recovery. As I configured and established a slight descent and reduced power to idle to start raising the nose the engine sputtered for a few seconds and totally quit. I applied full throttle and still nothing. My student announced your flight controls and I delegated all the checklists tasks to him while I flew the airplane to establish best glide and turn to the east to land in one of the fields lying east to west. I told him to changeover to tower frequency and [Advice ATC]. By the time he was announcing to tower; the engine came back alive after what felt like a long 30 seconds. I immediately turned to the airport and performed a normal climb to 4000 feet to ensure I make it across the water and clear the town in case the engine decided to quit again. I was also careful about reducing the power to idle until landing was assured at ZZZ. I entered left base around 1000 feet and stayed over the end of the runway to perform shallow S Turns to dissipate altitude to 600 feet before performing a forward slip to landing by taxiway 1. I believe the idle may be low and performing the power off stall may have slowed the rpm's enough to choke out the engine as it restarted when the nose was lower and the rpm's increased from the airflow causing it to windmill.