In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of N = 2 supergravity theories interpolating between all the single dilaton truncations of the SO(8) gauged N = 8 supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable choices of the parameters defining the N = 2 model, the supersymmetric solution features a higher free energy than the non-supersymmetric one. In the absence of additional selection rules, this would imply an instability of the supersymmetric configuration, hinting towards a possible supersymmetry breaking mechanism.