We consider a predator-prey model of planktonic population dynamics, of excitable character, living in an open and chaotic fluid flow, i.e., a state of fluid motion in which fluid trajectories are unbounded but a chaotic region exists that is restricted to a localized area. Despite that excitability is a transient phenomenon and that fluid trajectories are continuously leaving the system, there is a regime of parameters where the excitation remains permanently in the system, given rise to a persistent plankton bloom. This regime is reached when the time scales associated to fluid stirring become slower than the ones associated to biological growth.