Mesic savannas are dominated by trees that are strong resprouters caught in a frequent fire trap. Persistence within this fire trap has been described by a resprout curve of SizeNext ~ f(Pre-fire size), defined by the Michaelis-Menten function. A key feature of this resprout curve is a stable persistence equilibrium that represents the size of individual plants upon which a population will converge over successive inter-fire time steps under a given fire regime. Here, we contend that such a resprout curve does not adequately describe resprout tree dynamics in frequently burnt mesic savannas because it is constrained to an asymptote. We propose a new framework for modelling the resprout curve, which recognizes that local environmental stochasticity and growth patterns can interact to change the growth response function entirely, and thus more readily reflect the range of feasible resprout responses. Importantly, we define an unstable equilibrium representing the size above which individuals have escaped the fire trap and explore mechanisms that can shift an individual from persistence to escape. Through a case study from northern Australia, we confirm that our framework provides a simple yet practical approach to defining these critical aspects of savanna tree growth dynamics: persistence and escape.