Throughout the history of software, evolution has occurred in cycles of rise and fall driven by competition, and open-source software (OSS) is no exception. This cycle is accelerating, particularly in rapidly evolving domains such as web development and deep learning. However, the impact of competitive relationships among OSS projects on their survival remains unclear, and there are risks of losing a competitive edge to rivals. To address this, this study proposes a new automated method called ``Mutual Impact Analysis of OSS (MIAO)'' to quantify these competitive relationships. The proposed method employs a structural vector autoregressive model and impulse response functions, normally used in macroeconomic analysis, to analyze the interactions among OSS projects. In an empirical analysis involving mining and analyzing 187 OSS project groups, MIAO identified projects that were forced to cease development owing to competitive influences with up to 81% accuracy, and the resulting features supported predictive experiments that anticipate cessation one year ahead with up to 77% accuracy. This suggests that MIAO could be a valuable tool for OSS project maintainers to understand the dynamics of OSS ecosystems and predict the rise and fall of OSS projects.