A challenge with species that have disappeared from most of their range is to identify the correlates of local persistence. With species decimated by trade, site‐specific trapping risk is hard to capture by remotely accessed predictors. The recently split yellow‐crested cockatoo Cacatua sulphurea and citron‐crested cockatoo C. citrinocristata have undergone catastrophic declines due to habitat loss and especially trapping, and are now extinct in much of their former range across Indonesia. Of 144 sites on 30 islands known to contain the species in 1950, only 76 on 27 islands did so in 2017–2019, with many of the other 68 experiencing extinctions between 1985 and 2000. We compared socio‐ecological conditions such as forest cover and loss, human population density and infrastructure, and protected area status between the occupied and unoccupied sites, using ‘random forests’ within decreasing time intervals 1950–2015. Populations on Sulawesi and West Nusa Tenggara were more likely to become extinct than those on Sumba, Timor‐Leste and small remote islands. Sites retaining cockatoos had high proportions of tree cover, low road density and low human densities. The relative importance of these factors changed little over time, but road density and human density became respectively more and less important in recent years. The examination of local conditions at ‘false negative’ sites (where cockatoos survived contrary to model predictions) showed that, particularly in recent years, cockatoo survival has been promoted by site‐specific protection due to traditional beliefs, NGO activities, dedicated individual residents and local topographic barriers. Some of these local influences add complexity to the task of conserving cockatoo strongholds, but also offer exciting possibilities for low‐cost conservation prescriptions tailored to individual sites. Studies combining field and remotely sensed data, and examining false negative sites for beneficial location‐specific conditions, have broad application for the conservation of taxa with once‐large ranges.