According to the pilot of the retractable landing gear airplane, he retracted the landing gear after departure, however, the landing gear warning horn continued to sound. After multiple extensions and retractions in hopes of correcting the issue, he decided to continue the flight with the landing gear extended. The pilot reported that he made an approach at his destination airport, bounced the landing, and taxied to parking. He reported the aforementioned events to the operator, and further inspection revealed substantial damage to the firewall. Further inspection by the operator's mechanics, accompanied by the Federal Aviation Administration Aviation Safety Inspector, revealed that the landing gear warning horn sounded in the retracted position, as a result of an intermittent fault in the throttle position micro-switch.