Recently, deep neural network (DNN) accelerators have received considerable attention due to reduced cost and energy compared to mainstream GPUs. In order to further reduce energy consumption, the included memory (storing weights and intermediate computations) is operated at low voltage. However, this causes bit errors in memory cells, directly impacting the stored (quantized) DNN weights. This results in a significant decrease in CNN accuracy. In this paper, we tackle the problem of DNN robustness against random bit errors. By using a robust fixed-point quantization, training with aggressive weight clipping as regularization and injecting random bit errors during training, we increase robustness significantly, allowing energy-efficient DNN accelerators.