Neuromorphic computing systems are embracing memristors to implement high density and low power synaptic storage as crossbar arrays in hardware. These systems are energy efficient in executing Spiking Neural Networks (SNNs). We observe that long bitlines and wordlines in a memristive crossbar are a major source of parasitic voltage drops, which create current asymmetry. Through circuit simulations, we show the significant endurance variation that results from this asymmetry. Therefore, if the critical memristors (ones with lower endurance) are overutilized, they may lead to a reduction of the crossbar's lifetime. We propose eSpine, a novel technique to improve lifetime by incorporating the endurance variation within each crossbar in mapping machine learning workloads, ensuring that synapses with higher activation are always implemented on memristors with higher endurance, and vice versa. eSpine works in two steps. First, it uses the Kernighan-Lin Graph Partitioning algorithm to partition a workload into clusters of neurons and synapses, where each cluster can fit in a crossbar. Second, it uses an instance of Particle Swarm Optimization (PSO) to map clusters to tiles, where the placement of synapses of a cluster to memristors of a crossbar is performed by analyzing their activation within the workload. We evaluate eSpine for a state-of-the-art neuromorphic hardware model with phase-change memory (PCM)-based memristors. Using 10 SNN workloads, we demonstrate a significant improvement in the effective lifetime.