The relative importance of genetic, demographic, environmental, and catastrophic processes that maintain population bottlenecks has received little consideration. We evaluate the role of these factors in maintaining the Puerto Rican Parrot (Amazona vittata) in a prolonged bottleneck from 1973 through 2000 despite intensive conservation efforts. We first conduct a risk analysis, then examine evidence for the importance of specific processes maintaining the bottleneck using the multiple competing hypotheses approach, and finally integrate these results through a sensitivity analysis of a demographic model using life‐stage simulation analysis (LSA) to determine the relative importance of genetic, demographic, environmental, and catastrophic processes on population growth. Annual population growth has been slow and variable (1.0 ± 5.2 parrots per year, or an average λ = 1.05 ± 0.19) from 16 parrots (1973) to a high of 40–42 birds (1997–1998). A risk analysis based on population prediction intervals (PPI) indicates great risk and large uncertainty, with a range of 22–83 birds in the 90% PPI only five years into the future. Four primary factors (reduced hatching success due to inbreeding, failure of adults to nest, nest failure due to nongenetic causes, and reduced survival of adults and juveniles) were responsible for maintaining the bottleneck. Egg‐hatchability rates were low (70.6% per egg and 76.8% per pair), and hatchability increased after mate changes, suggesting inbreeding effects. Only an average of 34% of the population nested annually, which was well below the percentage of adults that should have reached an age of first breeding (41–56%). This chronic failure to nest appears to have been caused primarily by environmental and/or behavioral factors, and not by nest‐site scarcity or a skewed sex ratio. Nest failure rates from nongenetic causes (i.e., predation, parasitism, and wet cavities) were low (29%) due to active management (protecting nests and fostering captive young into wild nests), diminishing the importance of nest failure as a limiting factor. Annual survival has been periodically reduced by catastrophes (hurricanes), which have greatly constrained population growth, but survival rates were high under non‐catastrophic conditions. Although the importance of factors maintaining the Puerto Rican Parrot bottleneck varied throughout the 30‐year period of study, we determined their long‐term influence using LSA simulations to correlate variation in demographic rates with variation in population growth (λ). The bottleneck appears to have been maintained primarily by periodic catastrophes (hurricanes) that reduced adult survival, and secondarily by environmental and/or behavioral factors that resulted in a failure of many adults to nest. The influence of inbreeding through reduced hatching success played a much less significant role, even when additional effects of inbreeding on the production and mortality of young were incorporated into the LSA. Management actions needed to speed recovery include (1) continued nest guarding to minimize the effects of nest failure due to nongenetic causes; (2) creating a second population at another location on the island—a process that was recently initiated—to reduce the chance that hurricane strikes will cause extinction; and (3) determining the causes of the low percentage of breeders in the population and ameliorating them, which would have a large impact on population growth.