The pilot had not flown the aircraft or used the strip for about 4-5 weeks. As the strip had just been mown, the pilot walked, drove his vehicle and taxied the aircraft over it to check for obstructions or holes. The takeoff was uneventful and on the following landing roll, at about 40 knots, the pilot reported that he lowered the nosewheel onto the strip by relaxing the back pressure on the control column. Almost immediately, the aircraft reportedly became airborne again and the pilot held the control column back. On the subsequent touchdown, the nosegear leg failed and the aircraft skidded to rest on its nose. The pilot said that he could not find any obstructions or holes in the strip which could have caused the aircraft to bounce. It is assumed that on the second touchdown, the aircraft landed on its nosewheel first and the leg collapsed due to an overload failure. Despite promises to do so, the pilot failed to deliver the failed parts for inspection and determination of the mode of failure.