On-device learning remains a formidable challenge, especially when dealing with resource-constrained devices that have limited computational capabilities. This challenge is primarily rooted in two key issues: first, the memory available on embedded devices is typically insufficient to accommodate the memory-intensive back-propagation algorithm, which often relies on floating-point precision. Second, the development of learning algorithms on models with extreme quantization levels, such as Binary Neural Networks (BNNs), is critical due to the drastic reduction in bit representation. In this study, we propose a solution that combines recent advancements in the field of Continual Learning (CL) and Binary Neural Networks to enable on-device training while maintaining competitive performance. Specifically, our approach leverages binary latent replay (LR) activations and a novel quantization scheme that significantly reduces the number of bits required for gradient computation. The experimental validation demonstrates a significant accuracy improvement in combination with a noticeable reduction in memory requirement, confirming the suitability of our approach in expanding the practical applications of deep learning in real-world scenarios.