The parent company of Tuneup Masters Inc., Buena Park’s Cardis Corp., said that Bessemer Securities Corp. had withdrawn its offer to buy the car-tuneup chain. In a terse statement, Cardis didn’t say why the deal had fallen through, and executives could not be reached Tuesday. The auto parts chain has been under the protection of a federal bankruptcy court since May. The subsidiary, Newbury Park-based Tuneup Masters, is not in bankruptcy and is Cardis’ only profitable subsidiary. The $60-million sale to Bessemer had been set for a hearing in U.S. Bankruptcy Court in Los Angeles today. Cardis said its investment banker, New York’s Bear, Stearns & Co., is looking for another buyer.