Continuous Speaker Recognition (CSR) in noisy industrial environments poses unique challenges: models must continually adapt to newly enrolled users without forgetting previously learned speakers, all while operating under tight computational and memory constraints. In this paper, we introduce ICPG-CSR, an Industrial Compacting-Picking-Growing framework tailored for CSR on factory floors. ICPG-CSR integrates a Slim ResNet18 backbone trained on Mel-Frequency Cepstral Coefficients (MFCCs) with a three-phase continual learning loop: (1) Compacting, where magnitude-based pruning identifies a lean subnetwork of critical weights; (2) Picking, which masks and preserves these weights during subsequent updates; and (3) Growing, dynamically expanding model capacity only when performance drops below a preset threshold. Evaluated on a 50-speaker subset of VoxCeleb1 under a task-incremental protocol, ICPG-CSR achieves an average accuracy of 94.04% across ten sequential speaker-addition tasks, surpassing state-of-the-art replay, regularization, and memory-based baselines by over 40% points. Moreover, the full training sequence completes in under six hours on a single NVIDIA A100 GPU, demonstrating that dynamic capacity management can deliver both robustness and efficiency in real-time, resource-constrained industrial settings.