Abstract: Replay attacks are the most accessible threat to voice-controlled systems, and the acoustic cues that expose them are strongly modulated by the environment in which the attack is mounted. A detector deployed in the field therefore has to absorb new acoustic conditions over time, ideally without revisiting past recordings, since retaining speech indefinitely is both expensive and legally constrained. We frame this as Domain-Incremental Learning (DIL) over acoustic environments and present the first continual learning benchmark for multi-channel replay speech detection, evaluating a state-of-the-art beamformer-based detector over all 24 environment orderings of the ReMASC corpus with five seeds. Sequential fine-tuning forgets severely, raising the error rate on previously learned environments by 18.8 points. Elastic weight consolidation (EWC) halves forgetting but loses plasticity, gradient projection memory (GPM) is statistically indistinguishable from naive fine-tuning, and the proposed task-specific beamformer (TSB) that keeps one spatial front-end per environment significantly improves final and incremental accuracy. We further show that the last environment of the sequence dominates final performance. Code, results, and analysis are available at https://github.com/michaelneri/replay-speech-continual.