Keyword spotting (KWS) is an essential function that enables interaction with ubiquitous smart devices. However, in resource-limited devices, KWS models are often static and can thus not adapt to new scenarios, such as added keywords. To overcome this problem, we propose a Continual Learning (CL) approach for KWS built on Binary Neural Networks (BNNs). The framework leverages the reduced computation and memory requirements of BNNs while incorporating techniques that enable the seamless integration of new keywords over time. This study evaluates seven CL techniques on a 16-class use case, reporting an accuracy exceeding 95% for a single additional keyword and up to 86% for four additional classes. Sensitivity to the amount of training samples in the CL phase, and differences in computational complexities are being evaluated. These evaluations demonstrate that batch-based algorithms are more sensitive to the CL dataset size, and that differences between the computational complexities are insignificant. These findings highlight the potential of developing an effective and computationally efficient technique for continuously integrating new keywords in KWS applications that is compatible with resource-constrained devices.