The growing popularity of edge computing has fostered the development of diverse solutions to support Artificial Intelligence (AI) in energy-constrained devices. Nonetheless, comparatively few efforts have focused on the resiliency exhibited by AI workloads (such as Convolutional Neural Networks, CNNs) as an avenue towards increasing their run-time efficiency, and even fewer have proposed strategies to increase such resiliency. We herein address this challenge in the context of Bit-line Computing architectures, an embodiment of the in-memory computing paradigm tailored towards CNN applications. We show that little additional hardware is required to add highly effective error detection and mitigation in such platforms. In turn, our proposed scheme can cope with high error rates when performing memory accesses with no impact on CNNs accuracy, allowing for very aggressive voltage scaling. Complementary, we also show that CNN resiliency can be increased by algorithmic optimizations in addition to architectural ones, adopting a combined ensembling and pruning strategy that increases robustness while not inflating workload requirements. Experiments on different quantized CNN models reveal that our combined hardware/software approach enables the supply voltage to be reduced to just 650mV, decreasing the energy per inference up to 51.3%, without affecting the baseline CNN classification accuracy.