As an emerging technology, sensor networks provide the ability to accurately monitor the characteristics of wide geographical areas over long periods of time. The lifetime of individual nodes in a sensor network depends strongly on the leakage power that the nodes dissipate in the idle state, especially for low-throughput applications. With the introduction of advanced low power design techniques, such as sub-threshold voltage design styles, and the migration of fabrication processes to smaller technology generations, variability in leakage power dissipation of the sensor nodes will lead to increased variability in their lifetimes. In this paper, we analyze how this increased variability in the lifetime of individual sensor nodes affects the performance and lifetime of the network as a whole. We demonstrate how sensor network designers can use the proposed analysis framework to trade-off the cost of a sensor network deployment with the performance it offers. Our results indicate that up to 37% improvement in the critical lifetime of a sensor network (defined as the expected time at which the sensor network becomes disconnected) can be obtained over a baseline design with a 20% increase in the cost of the individual sensor nodes.