A Flight School Instructor reported a fuel servo failure resulting in engine failure and return to departure airport. Reporter stated this flight school's aircraft have repeatedly experienced this problem.

Narrative

I experienced an engine failure. The flight was a normal pattern work training flight that began with a routine flight to ZZZ1 followed by two laps in the pattern. In the downwind at ZZZ1 on the third lap I felt a small drop in RPM. I asked the student if they had pulled the throttle to which they answered yes. Out of an abundance of caution I decided to return to ZZZ early because I wasn't confident in his answer. We climbed to 3000 feet and with the mixture full rich. We experienced extreme oil pressure abnormalities and oil pressure in the red on the return. This turned out to be a sensor failure according to Maintenance. Approximately 5 miles from ZZZ the fuel servo failed causing flooding of the engine. Fuel flow got stuck around 9GPH regardless of throttle / RPM setting. As we reduced power for descent fuel flow remained the same and caused flooding of the engine. This led to engine roughness on downwind and extreme engine roughness on base to final. The aircraft also reached approximately 700RPM while in flight and 600RPM around the threshold. On touchdown the engine failed completely causing us to be unable to clear the runway without being towed. Maintenance found that this was due to a fuel servo failure causing the engine to be flooded with fuel and ultimately resulting in engine failure. According to the director of maintenance if I had not increased power on final when I did the engine would have failed earlier. This is one of many fuel servo failures ZZZ has had over the last few months.