Homelessness prevention and rapid rehousing (RRH) programs are increasingly important components of the homeless assistance system in the United States. Yet, there are key gaps in knowledge about the dynamics of the utilization of these programs, with scant attention paid to examining the duration of homelessness prevention and RRH service episodes or to patterns of repeated use of these programs over time. To address these gaps, we use data from the U.S. Department of Veterans Affairs' (VA) Supportive Services for Veteran Families (SSVF) program-the largest program in the country providing homelessness prevention and RRH services-to assess the relationship between individual and program-level factors and exits to stable housing, length of service episodes, and patterns of repeated service use over time. We analyze data for a primary cohort of 570,798 of Veterans who received SSVF services during Fiscal Years (FY) 2012-2021, and for separate cohorts of Veterans who received SSVF prevention and RRH services, respectively, during FY 2016-2021. We find that participants' income, indicators of their health status, their use of other VA homeless programs, and rurality are consistent predictors of our outcomes. These findings have implications for how to allocate homelessness prevention and RRH resources in the most efficient manner to help households maintain or obtain stable housing.