Resistive random-access memory (ReRAM)-based processing-in-memory (PIM) accelerator is a promising platform for processing massively memory intensive matrix-vector multiplications of neural networks in parallel domain, due to its capability of analog computation, ultra-high density, near-zero leakage current, and nonvolatility. Despite many advantages, ReRAM-based accelerators are highly error-prone due to limitations of technology fabrication that lead to process variations and defects. These limitations degrade the accuracy of deep convolutional neural networks (CNNs) (Deep CNNs) running on PIM accelerators. While these CNNs accelerators are widely deployed in safety-critical systems, their vulnerability to fault is not well explored. In this article, we have developed a fault-injection framework to investigate the vulnerability of large-scale CNNs at both software- and hardware-level of inference phases. Faulty ReRAM devices are another reliability challenges due to significant degradation of classification accuracy when CNN parameters are mapped to the accelerators. To investigate this challenge, we map the CNN learning parameter to the ReRAM crossbar and inject faults into crossbar arrays. The proposed framework analyzes the impact of stuck-at high (SaH) and stuck-at low (SaL) fault models on different layers and locations of CNN learning parameters. By performing extensive fault injections, we illustrate that the vulnerability behavior of ReRAM-based PIM accelerator for CNNs is greatly impressible to the types and depth of layers, the location of the learning parameter in every layer, and the value and types of faults. Our observations show that different models have different vulnerabilities to faults. Specifically, we show that SaL further reduces classification accuracy than SaH.