SR20 Flight Instructor reported the aircraft engine shut down uncommanded two times during taxi. After the second shut down and subsequent restart; aircraft was taxied back to the ramp.

Narrative

While taxiing the Cirrus SR20 aircraft for a Discovery Flight with a participant onboard; the engine suddenly shut down. I immediately reported the situation to Ground and followed their instructions. Initially; I considered the possibility that the Discovery Flight participant might have inadvertently operated a control I hadn't noticed during the experience. Following the checklist procedures; I attempted to restart the engine. The restart was successful; and I resumed taxiing toward the runway.However; upon reaching Runway XX at ZZZ Airport and preparing for takeoff; the engine shut down again. I promptly informed the ATC Tower of the situation and notified them that I was unable to vacate the runway on my own. I attempted to restart the engine again using the Hot Start procedure; as outlined in the checklist; but all three attempts were unsuccessful.To ensure our safety; the Airport Manager arrived at the scene to check on us. To clear the runway; the Discovery Flight participant; the Airport Manager; and I worked together to push the aircraft to Taxiway 1 successfully. Afterward; the Airport Manager contacted a towing service to safely relocate the aircraft. Shortly after; the towing service arrived at the scene; accompanied by the flight school's owner. The Owner attempted to restart the engine; and this time the engine was successfully started. The aircraft was then taxied back to the ramp.While returning to the ramp; the Owner explained some unique characteristics of the Lycoming engine installed in the aircraft. While it was appropriate to follow the procedures outlined in the Pilot's Operating Handbook (POH); he shared practical advice based on his experience to better operate this specific engine model. This greatly enhanced my understanding of the engine and provided valuable insights for handling similar situations in the future.Fortunately; there were no injuries or damage to the aircraft during this incident. However; this event emphasized the importance of gaining a deeper understanding of the specific characteristics of this engine type and accumulating operational experience.