Among felids worldwide, only 6 of 38 species have stable or increasing populations, and most felid species are threatened by anthropogenic influences, especially habitat loss and fragmentation. We documented changes in genetic diversity in an isolated, reintroduced population of bobcats on Cumberland Island (CUIS), Georgia, USA, compared to another bobcat population on Kiawah Island, South Carolina, USA, that was naturally established and experiences limited immigration from the mainland. The CUIS population declined from 32 reintroduced bobcats in 1989 to 10–24 individuals during 2012–2019, and observed heterozygosity declined from 0.742 to 0.634 (SD = 0.240). Observed heterozygosity of bobcats on Kiawah was 0.699 (SD = 0.153). We estimated that one bobcat immigrated to Kiawah Island every 5.3 years. We compared the predictions of a novel population viability analysis (PVA) to empirical estimates of abundance and genetic diversity on CUIS and used our PVA to identify management actions that are likely to support long-term viability. Mean heterozygosity from the PVA (0.588, SD = 0.065) was within 1 standard deviation of the empirical estimate. The PVA estimated the population would decline following population restoration due to loss of genetic diversity and inbreeding depression. Translocations of one female every four years would stabilize allele heterozygosity similar to the Kiawah Island population, but even translocations of two females every two years would not restore heterozygosity to founder levels. The PVA predicted no management action would result in a one in five probability of extinction within 50 years of reintroduction, but all translocation strategies nearly eliminated extinction risk through 100 years.