Model compression via quantization and sparsity enhancement has gained an immense interest to enable the deployment of deep neural networks (DNNs) in resource-constrained edge environments. Although these techniques have shown promising results in reducing the energy, latency and memory requirements of the DNNs, their performance in non-ideal real-world settings (such as in the presence of hardware faults) is yet to be completely understood. In this paper, we investigate the impact of bit-flip and stuck-at faults on activation-sparse quantized DNNs (QDNNs). We show that a high level of activation sparsity comes at the cost of larger vulnerability to faults. For instance, activation-sparse QDNNs exhibit up to 17.32% lower accuracy than the standard QDNNs. We also establish that one of the major cause of the degraded accuracy is sharper minima in the loss landscape for activation-sparse QDNNs, which makes them more sensitive to perturbations in the weight values due to faults. Based on this observation, we propose the mitigation of the impact of faults by employing a sharpness-aware quantization (SAQ) training scheme. The activation-sparse and standard QDNNs trained with SAQ have up to 36.71% and 24.76% higher inference accuracy, respectively compared to their conventionally trained equivalents. Moreover, we show that SAQ-trained activation-sparse QDNNs show better accuracy in faulty settings than standard QDNNs trained conventionally. Thus the proposed technique can be instrumental in achieving sparsity-related energy/latency benefits without compromising on fault tolerance.