  We study the fate of two-centered D1-D5 systems on T^4 away from the singular
supergravity point in the moduli space. We do this by considering a background
D1-D5 black hole with a self-dual B-field moduli turned on and treating the
second center in the probe limit in this background. We find that in general
marginal bound states at zero moduli become metastable at finite B-moduli,
demonstrating a breaking of supersymmetry. However, we also find evidence that
when the charges of both centers are comparable, the effects of supersymmetry
breaking become negligible. We show that this effect is independent of string
coupling and thus it should be possible to reproduce this in the CFT at weak
coupling. We comment on the implications for the fuzzball proposal.
