On September 29, 2013, at 2050 central daylight time, a Piper PA-28-181, N31688, experienced a hard landing short of the runway at the Algona Municipal Airport (AXA), Algona, Iowa, following a loss of engine power. The private pilot and flight instructor were not injured. The airplane sustained substantial damage to both wings. The airplane was registered to Okoboji Flyers LLC, and operated by the private pilot as a 14 Code of Federal Regulations Part 91 instructional flight. Night visual meteorological prevailed for the flight, which was not operated on a flight plan. The accident leg of the flight originated from the Estherville Municipal Airport (EST), Estherville, Iowa, at 1800. The pilot departed Spencer, Iowa, and flew to EST where he picked up his flight instructor. The pilot stated the purpose of the flight was to complete a flight review. He reported the airplane contained 34 gallons of fuel prior to takeoff and during the flight he switched fuel tanks every 30 minutes. After departing EST, they flew south then east for about 1 hour. Based on the distance from EST and the amount of fuel remaining, the pilot elected to fly to a closer airport, AXA, to obtain fuel prior to returning to EST. About 38 miles northeast of AXA, the pilot listened to the automated weather observation system (AWOS) for the airport. He stated there were no notices to airmen (NOTAMs) on the AWOS. They continued to AXA and the engine began to sputter when they were approximately 1 mile from the airport. The pilot switched fuel tanks and the engine regained power. He stated they circled the airport 3 times as they tried to turn on the runway lights. On the fourth pass, the engine lost power. The pilot made a hard landing short of the approach end of runway 12. A postaccident examination of the airplane revealed no useable fuel remained in the fuel tanks. The airport manager stated the airport was closed between September 16, 2013 and October 9, 2013, due to runway construction. He stated they issued a NOTAM, crossed out the runway numbers, shut the airport beacon light off, and deactivated the pilot controlled runway lights. The airport manager stated they put the runway closure information on the AWOS, but it kept dropping off.