The pilot of the airplane reported that, while on short final to land, the airplane experienced a sudden loss of airspeed due to windshear. The pilot continued the approach and reported that he flared too high, and the airplane bounced during landing. He elected to go around, and during the second landing the airplane bounced again. During the third landing attempt, the pilot successfully landed the airplane. The airplane sustained substantial damage to the forward fuselage undercarriage. The pilot reported there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. The automated weather observation station located on the airport reported that, about the time of the accident, the wind was from 330° at 12 knots. The pilot reported that during the accident flight, the wind was at 12 knots, gusting to 20 knots. The airplane landed on runway 30.