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 resource war model where incumbent and opposition invest in stocks of military arsenal and the opposition strategically chooses the timing of attack. We show that a random increase in the resource stock allows the incumbent stay in power longer by lowering the probability of coup success and increasing the time to attack. We test this prediction with a novel empirical analysis based on duration models and extended data on discoveries of giant oil and gas fields. Our results show that an increase in the stock of natural resources lowers the hazard faced by an autocrat; resource discoveries thus appear to have a stabilizing effect on autocratic regimes.