  We analyze the stability of the moduli at the quantum level in an open-string
model realizing the $\mathcal{N}=2\to \mathcal{N}=0$ spontaneous breaking of
supersymmetry in four-dimensional Minkowski spacetime. In the region of moduli
space where the supersymmetry breaking scale is lower than the other scales, we
identify vanishing minima of the one-loop effective potential, up to
exponentially small corrections. In these backgrounds, the spectrum satisfies
Bose-Fermi degeneracy at the massless level.
