The introduction of mammalian predators to oceanic islands has led to dramatic declines in the abundance of many native species. Conservation management of these species often relies on low-cost predator control techniques that can be implemented over large scales. Assessing the effectiveness of such management techniques is difficult, but using population viability analyses (PVA), which identify the population growth rate (λ) and extinction risk of threatened species, may offer a solution. PVA provide the opportunity to compare the relative effectiveness of various management options and can identify knowledge gaps to prioritize research efforts. We used PVA to assess the population viability of whio (Hymenolaimus malacorhynchos), a rare riverine duck endemic to New Zealand. Current populations are threatened by introduced mammalian predators and are rapidly declining in both distribution and abundance. Whio conservation management is dominated by large-scale, low-intensity predator control, targeting introduced stoats (Mustela erminea). There is evidence that such control increases whio productivity but it is unknown if this increase is sufficient for long-term population persistence. We undertook a stochastic PVA to assess the viability of whio populations under different management scenarios using data obtained from a 6-year study of whio demographic responses to predator control. Populations with no predator control and low productivity will rapidly decline to extinction. Increasing productivity through predator control increased population viability but populations still showed a declining trajectory. A perturbation analysis showed that the growth rate of whio populations was largely driven by adult survival. Therefore, future research should target obtaining more robust estimates of adult survival, particularly how it is affected by predator control. Overall, our analysis indicated that large-scale predator control increases the short-term viability of whio populations but is insufficient for long-term population persistence.