Brain-machine interfaces (BMIs) are expanding beyond clinical settings thanks to advances in hardware and algorithms. However, they still face challenges in user-friendliness and signal variability. Classification models need periodic adaptation for real-life use, making an optimal re-training strategy essential to maximize user acceptance and maintain high performance. We propose TOR, a train-on-request workflow that enables user-specific model adaptation to novel conditions, addressing signal variability over time. Using continual learning, TOR preserves knowledge across sessions and mitigates inter-session variability. With TOR, users can refine, on demand, the model through on-device learning (ODL) to enhance accuracy adapting to changing conditions. We evaluate the proposed methodology on a motor-movement dataset recorded with a non-stigmatizing wearable BMI headband, achieving up to 92% accuracy and a re-calibration time as low as 1.6 minutes, a 46% reduction compared to a naive transfer learning workflow. We additionally demonstrate that TOR is suitable for ODL in extreme edge settings by deploying the training procedure on a RISC-V ultra-low-power SoC (GAP9), resulting in 21.6 ms of latency and 1 mJ of energy consumption per training step. To the best of our knowledge, this work is the first demonstration of an online, energy-efficient, dynamic adaptation of a BMI model to the intrinsic variability of EEG signals in real-time settings.