In the finite-horizon repeated Prisoner's Dilemma, a compelling backward induction argument shows that rational players will defect in every round, following the uniquely optimal Nash equilibrium path. It is frequently asserted that cooperation gradually declines when a Prisoner's Dilemma is repeated multiple times by the same players, but the evidence for this is unconvincing, and a classic experiment by Rapoport and Chammah in the 1960s reported that cooperation eventually recovers if the game is repeated hundreds of times. They also reported that men paired with men cooperate almost twice as frequently as women paired with women. Our conceptual replication with Prisoner's Dilemmas repeated over 300 rounds with no breaks, using more advanced, computerized methodology, revealed no decline in cooperation, apart from endgame effects in the last few rounds, and replicated the substantial gender difference, confirming, in the UK, a puzzling finding first reported in the US in the 1960s.