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We consider the dynamical stability of a static brane model that incorporates a three-index antisymmetric tensor field and has recently been proposed [1, 2] as a possible solution to the cosmological constant problem. Ultimately, we are able to establish the existence of time-dependent, purely gravitational perturbations. As a consequence, the static solution of interest is `dangerously' located at an unstable saddle point. This outcome is suggestive of a hidden fine tuning in what is an otherwise self-tuning model.