The pilot was conducting touch-and-go practice takeoffs and landings in the airport traffic pattern. She reported that during the landing flare for the final landing, her seat slid aft. The airplane ballooned and subsequently landed hard, resulting in substantial damage to the engine firewall and cabin floor structure. The accident airplane make/model was the subject of a Federal Aviation Administration (FAA) airworthiness directive (AD) regarding seat slippage, issued three years prior to the accident. Review of the airplane's maintenance logs revealed that the airplane had received the inspections required by the AD, and examination of the seat rail and latching mechanism by an FAA inspector revealed no anomalies.