PA28 Flight Instructor reported a loss of engine power during simulated engine out procedures training with a student. The Instructor landed at a nearby abandoned airfield where the aircraft was inspected with no abnormalities found.

Narrative

A CFI during a training flight in a PA28 was performing simulated engine out procedures training. After an extended period at idle power setting; the CFI advanced the throttle and noted a reduction in climb power. Out of precaution; the CFI made the determination to land at the abandoned airfield directly beneath the aircraft. The CFI made a normal landing under normal operating procedures without any damage to the aircraft or persons or property. I contacted Local Authorities who escorted us to the airfield to secure the aircraft for the evening and pick up the crew. We conducted a thorough review of the FARs and determined there was no NTSB reporting required and no FAR prohibiting landing on an abandoned airfield.The day following; I; the Aircraft Operator and Commercial Pilot; with an A&P Consultant conducted a thorough assessment of the aircraft. I found no damage to the aircraft or abnormalities. I conducted an operational check of all aircraft systems and all checked good. In addition; I conducted multiple engine run ups with maximum power settings with no indication of power abnormalities. I concluded after a thorough examination the aircraft was safe for flight. I conducted a comprehensive risk management assessment for a departure flight which included a FOD walk down of the runway; noted the abort takeoff distance; confirmed runway length and posted a spotter aircraft overhead if needed for assistance. I performed a soft field takeoff procedure and received normal takeoff performance indications. I remained over the airfield and climbed to above 5;000 feet before departing the field; flying to the closest airport 12 miles away and delivered the aircraft to the aircraft maintenance shop on the airport for further assessment. In summary; I and the maintenance personnel involved; assume the long period at idle in flight could have caused a buildup of ice in the carburetor and for this reason we were unable to duplicate any power loss on the engine the following day.