We analyze the lifetime of clustered sensor networks with decentralized binary detection under a physical layer quality-of-service (QoS) constraint, given by the maximum tolerable probability of decision error at the access point (AP). In order to properly model the network behavior, we consider four different distributions (exponential, uniform, Rayleigh, and lognormal) for the lifetime of a single sensor. We show the benefits, in terms of longer network lifetime, of adaptive reclustering. We also derive an analytical framework for the computation of the network lifetime and the penalty, in terms of time delay and energy consumption, brought by adaptive reclustering. On the other hand, absence of reclustering leads to a shorter network lifetime, and we show the impact of various clustering configurations under different QoS conditions. Our results show that the organization of sensors in a few big clusters is the winning strategy to maximize the network lifetime. Moreover, the observation of the phenomenon should be frequent in order to limit the penalties associated with the reclustering procedure. We also apply the developed framework to analyze the energy consumption associated with the proposed reclustering protocol, obtaining results in good agreement with the performance of realistic wireless sensor networks. Finally, we present simulation results on the lifetime of IEEE 802.15.4 wireless sensor networks, which enrich the proposed analytical framework and show that typical networking performance metrics (such as throughput and delay) are influenced by the sensor network lifetime.