Scientific software includes end-user applications, modelling tools, research software for publications, and production systems for real users. It plays a key role across various scientific disciplines by enabling large-scale computation, simulation, and data analysis. Unlike commercial software, scientific software is often developed in dynamic research environments with limited engineering practices, documentation, or testing. This makes it fragile and difficult to reproduce results, even when code and data are available, conditions in which Reproducibility Debt (RpD) accumulates. This paper presents the Reproducibility Debt Management Framework (RpD-MF), which is grounded in evidence from a systematic literature review, practitioner interviews, and a global survey. Central to the framework is a probabilistic cause-effect model that maps how technical, human, and organisational factors contribute to RpD. The framework is designed to help researchers and research software engineers identify, monitor, and prevent RpD, providing practical guidance to support sustainable and reproducible scientific software development.