His next fight came three months later against Frankie Duarte, whom he had knocked out in a 1977 bout. The North American Boxing Federation (NABF) bantamweight championship was at stake, along with California's title in the division. Despite a left eye that had a cut over it, Dávila was leading on the judges' scorecards entering the 10th round. With 51 seconds left in the round, a doctor stopped the bout due to the cut, giving a technical knockout win to Duarte. Dávila filed an official protest, seeking to have the result overturned. He claimed that an accidental headbutt during round four caused the cut; under the rules of the NABF, fights halted after three rounds went to a judges' decision. The protest was voted on in July by California's State Athletic Commission; the voters deadlocked 3–3, leaving the result unchanged. In a bout held at the Great Western Forum in Inglewood, California on November 3, 1987, against Mexico's Juan Estrada, Dávila suffered an accidental headbutt and was given the victory through a technical decision.