Captive breeding and translocation, whereby selected individuals are used to supplement or re‐establish failing populations, are powerful tools for conserving threatened fauna. These tools, however, are rarely successful at establishing self‐sustaining populations that can survive without ongoing human assistance. The maintenance of genetic diversity and demographic security in captivity, or following wildlife translocation events, is important for improving the long‐term effectiveness of threatened species recovery efforts around the world. Routine population monitoring using hypervariable genetic markers represents a promising technique for evaluating the effect of established management practices on population structure and genetic diversity across various spatial and temporal scales. In this study, we employed a data set of 1,068 single nucleotide polymorphisms to conduct a comprehensive survey of population structure and genetic diversity in greater bilbies (Macrotis lagotis) held at 13 zoos and wildlife sanctuaries across Australia between August 1996 and December 2016. We observed significant genetic structuring across the study sites, consistent with the limited exchange of animals between independently managed facilities. The majority of variation, however, still occurred at the level of individual bilbies (75%, P < 0.001). We also uncovered evidence for an ongoing loss of genetic diversity in some conservation‐fenced populations, despite a slight excess of heterozygosity across the sampling sites as a whole. Maintaining the genetic health of bilbies in captivity or following translocation will therefore require stakeholders to focus on reducing individual mortality, and maintaining genetic connectivity across all existing populations through the regular exchange of selected individuals. As such, admixture is expected to play an increasingly important role in future conservation programs. © 2019 The Authors. Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.