Automated respiratory sound classification enables continuous, non-invasive respiratory assessment, yet long-term deployment remains challenging due to domain shifts from evolving recording devices and acquisition periods. When privacy and governance regulations prohibit replaying historical data, sequential learning easily overwrites previously acquired knowledge. Preserving dedicated domain experts prevents parameter interference, but selecting the correct expert at inference is difficult under overlapping acoustic distributions and absent domain labels. To resolve this dilemma, we propose APRIL, an exemplar-free domain-incremental framework for RSC. Built on a shared frozen BEATs backbone, APRIL sequentially inherits and isolates low-rank experts to enable new-domain adaptation without altering earlier models. A multi-level prototype router retrieves the top-two candidate experts and dynamically selects the final model by integrating domain-routing posteriors with classification confidence, adaptively weighted by matching ambiguity. We establish standardized device- and temporal-incremental benchmarks on the ICBHI and SPRSound datasets across forward and reversed domain orders. Evaluated over five random seeds, APRIL consistently achieves the highest final-session average Score among compared continual learning approaches, reaching 64.4% and 65.4% on ICBHI, and 83.1% and 82.2% on SPRSound under forward and reversed sequences, respectively. Crucially, average forgetting remains under 1.0% across all protocols, demonstrating robust domain adaptation and long-term knowledge retention without data replay. Overall, APRIL offers a reliable and privacy-preserving paradigm for deploying continuous respiratory sound classification across real-world healthcare settings.

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