Non-Volatile Memories (NVMs) such as Resistive RAM (RRAM) are used in neuromorphic systems to implement high-density and low-power analog synaptic weights. Unfortunately, an RRAM cell can switch its state after reading its content a certain number of times. Such behavior challenges the integrity and program-once-read-many-times philosophy of implementing machine learning inference on neuromorphic systems, impacting the Quality-of-Service (QoS). Elevated temperatures and frequent usage can significantly shorten the number of times an RRAM cell can be reliably read before it becomes absolutely necessary to reprogram. We propose an architectural solution to extend the read endurance of RRAM-based neuromorphic systems. We make two key contributions. First, we formulate the read endurance of an RRAM cell as a function of the programmed synaptic weight and its activation within a machine learning workload. Second, we propose an intelligent workload mapping strategy incorporating the endurance formulation to place the synapses of a machine learning model onto the RRAM cells of the hardware. The objective is to extend the inference lifetime, defined as the number of times the model can be used to generate output (inference) before the trained weights need to be reprogrammed on the RRAM cells of the system. We evaluate our architectural solution with machine learning workloads on a cycle-accurate simulator of an RRAM-based neuromorphic system. Our results demonstrate a significant increase in inference lifetime with only a minimal performance impact.