Financial markets are inherently non-stationary, exhibiting frequent regime shifts and structural changes that render traditional Portfolio Management (PM) approaches ineffective. Existing remedies, such as rolling-window retraining and naive online fine-tuning, are hindered by high computational costs and insufficient knowledge utilization, respectively, resulting in low returns and limited adaptability. Continual learning (CL) offers a promising paradigm by enabling trading agents to accumulate and transfer knowledge across sequential tasks. In this paper, we propose \textbf{Re}gime-aware \textbf{C}ontinual \textbf{A}daptive \textbf{P}ortfolio management (\textbf{ReCAP}), a novel framework that integrates CL into PM to address the challenges of dynamic financial environments. ReCAP employs an adaptive regime detection module to segment historical market data into variable-length regimes, enabling regime-specific learning of policy vectors and the construction of a policy library. During continual trading, a regime-gate module adaptively combines policy vectors from the library based on the current market state, facilitating rapid adaptation to newly detected regimes. Only the regime-gate and the current regime's policy vector are continually updated to preserve useful knowledge effectively. Extensive experiments on five real-world datasets demonstrate that ReCAP consistently outperforms popular baselines, achieving superior returns in long-term investment horizons and rapid adaptation to regime shifts.