Medication recommendation is a crucial task in healthcare, especially for patients with complex medical conditions. However, existing methods often struggle to effectively balance the reuse of historical medications with the introduction of new drugs in response to the changing patient conditions. In order to address this challenge, we propose an Adaptively Responsive network for Medication Recommendation (ARMR), a new method which incorporates 1) a piecewise temporal learning component that distinguishes between recent and distant patient history, enabling more nuanced temporal understanding, and 2) an adaptively responsive mechanism that dynamically adjusts attention to new and existing drugs based on the patient's current health state and medication history. Experiments on the MIMIC-III and MIMIC-IV datasets indicate that ARMR has better performance compared with the state-of-the-art baselines in different evaluation metrics, which contributes to more personalized and accurate medication recommendations. The source code is publicly avaiable at: https://github.com/seucoin/armr2.