Globally, fire maintains many mesic habitats in an open canopy state by killing woody plants while reducing the size of those able to resprout. Where fire is frequent, tree saplings are often suppressed by a "fire trap" of repeated topkill (death of aerial biomoass) and resprouting, preventing them from reaching adult size. The ability to tolerate repeated topkill is an essential life-history trait that allows a sapling to persist until it experiences a long fire-free interval, during which it can escape the fire trap. We hypothesized that persistence in the fire trap results from a curvilinear relationship between pre-burn size and resprout size, which causes a plant to approach an equilibrial size in which post-fire biomass recovery is equal to fire-induced biomass loss. We also predicted that the equilibrial stem size is positively related to resource availability. To test these hypotheses, we collected data on pre-burn and resprout size of five woody plant species at wetland ecotones in longleaf pine savanna subjected to frequent burning. As expected, all species exhibited similar curvilinear relationships between pre-burn size and resprout size. The calculated equilibrial sizes were strong predictors of mean plant size across species and growing conditions, supporting the persistence equilibrium model. An alternative approach using matrix models yielded similar results. Resprouting was less vigorous in dry sites than at wet sites, resulting in smaller equilibrial stem sizes in drier sites; extrapolating these results provides an explanation for the absence of these species in xeric uplands. This new framework offers a straightforward approach to guide data collection for experimental, comparative, and modeling studies of plant persistence and community dynamics in frequently burned habitats.