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Open-source projects do not exist in a vacuum. They benefit from reusing other projects and themselves are being reused by others, creating complex networks of interdependencies, i.e., software ecosystems. Therefore, the sustainability of projects comprising ecosystems may no longer by determined solely by factors internal to the project, but rather by the ecosystem context as well. In this paper we report on a mixed-methods study of ecosystem-level factors affecting the sustainability of open-source Python projects. Quantitatively, using historical data from 46,547 projects in the PyPI ecosystem, we modeled the chances of project development entering a period of dormancy (limited activity) as a function of the projects' position in their dependency networks, organizational support, and other factors. Qualitatively, we triangulated the revealed effects and further expanded on our models through interviews with project maintainers. Results show that the number of project ties and the relative position in the dependency network have significant impact on sustained project activity, with nuanced effects early in a project's life cycle and later on.