Continuously delivering valuable software is a core principle of agile software development (ASD). In practice, value delivery is often impeded by several key issues, including low customer involvement, volatile requirements, technical debt, delivery pressure, excessive rework, or meeting overhead, which affect the product or the process. Despite their negative influence, the different consequences for the delivered value remain to be better understood. In addition, a collection of measures to help practitioners adapt to these issues is missing, as previous work only offers limited guidance on how to mitigate them. To address this situation, we conducted 19 semi-structured expert interviews to identify the consequences of key issues for value delivery and empirically derive measures to adapt to these issues. We find 34 value-reducing consequences, which primarily affect product quality and capabilities, delivery timeliness, and process efficiency. We also develop a collection of 48 measures to address the issues, including procedural changes, process artifacts and roles, technical means, and different ways to approach customers. With our work, we provide practitioners with actionable measures to adapt to issues encountered in daily practice and avoid their value-reducing consequences, thereby facilitating continuous value delivery. For research, we extend knowledge on the dark side of ASD by illustrating how key issues affect the delivered value, which was less regarded in related studies. In addition, we encourage future investigations into how micro-tailoring fosters sustained value delivery, along with examinations of resilience engineering in the context of ASD to improve the performance of software development processes.