Empirical literature remains largely inconclusive as to whether resource abundance has significant political effects. In this paper we revisit the "political resource curse" by studying the effect of natural resource discoveries on the duration of autocratic leadership. We first present a dynamic stochastic model of a resource-driven coup. We extend the existing conflict models by considering both the timing of attack on the regime and the probability of its success. Both the incumbent and opposition invest in military arsenal which determines the probability of winning, while the opposition also strategically chooses when to stage a coup. We show that a random resource discovery allows the incumbent to stay in power longer by delaying the attack but also by reducing the probability of coup success under specific conditions. We test these hypotheses with a novel empirical analysis based on duration models and data on discoveries of giant oil and gas fields going back to as far as 1868. Our results show that a large hydrocarbon discovery lowers the hazard faced by an autocrat by 30 - 50%. The delay of the coup is the main driving force behind the stabilizing effect of discoveries in autocratic regimes.