Understanding long-term trajectories of restored coral populations requires sufficient knowledge of population demography. To better understand these dynamics, we construct a size-structured density-dependent integral projection model of a corymbose coral population calibrated to empirical data, and evaluate the resulting long-term dynamics. In the basic model, we catalogued three model pathologies that must be accounted for when projecting coral populations into the future, namely: (1) unrealistically high abundance of coral recruits in the absence of post-settlement density dependence, (2) intermittent occurrences of ‘impossible’ coral abundances exceeding 100% coral cover in the absence of adult density dependence, and (3) unrealistically rapid growth rates to maturity in juvenile corals. We provide the critical functional forms necessary to address these pathologies when data are available and explore which parameter values allow for long-term population persistence. We found that coral dynamics depend most on parameters related to larval settlement and recruitment, but also on high mortality in early life stages. We present a beta version of a web application of our model, allowing users to specify parameter values and allowing coral demographers and reef managers to explore what biological processes are most likely to drive long-term population persistence in restored coral populations.