Despite efforts to increase investment in Indigenous health and well-being in the United States, disparities remain. The way in which health-promoting organizations are funded is one key mechanism driving the systemic, long-term health disparities experienced by Indigenous people in the US. Using Indigenous-led community-based organizations (ICBOs) that provide psychosocial care as a case study, we highlight multiple ways in which policies that regulate the external funding that ICBOs depend on must change to promote equity and allow the organizations to flourish and address unmet psychosocial needs for Indigenous community members. We use a system dynamics approach to discuss how "capability traps" arise from a misfit between external funding regulations and organizations' needs for sustainability and effective care provision. We provide suggestions for reforming funding policies that focus on improving ICBO sustainability.