In Lord of the Flies, why does Jack deny that the beast is dead?

Jack is authority and power and control. The best way for him and his band to keep their power, is through fear. Jack uses fear to hold his power and to continue to wield it. If he convinces the others that the beast is still alive, he keeps fear alive. If he keeps fear alive, he keeps his power, for he and his group will protect the others from what they are unable to fight alone.

Of course, this is nothing new in the history of manunkind. Regimes from the beginning of time and up to today have wrested and maintained power by instilling fear in the masses. Once the masses are properly frightened, they will do anything to keep themselves and their families safe. Thus we have militias and war parties and armies.

This is one of the main themes of the novel. The boys are on the island because of a catastrophic war the ferocity of which was no doubt stoked by the fear mongers and power grabbers and the abusers of power. The island is the world in microcosm, and the forces that made the larger war are re-enacted by the boys, for though they are small humans, they are humans nonetheless.