The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a relatively accessible test case of the subtleties of superstring perturbation theory in the RNS formalism. In the present paper, we calculate the relevant amplitudes in the pure spinor approach to superstring perturbation theory, and show that the regulator used in computing loop amplitudes in the pure spinor formalism leads to subtleties somewhat analogous to the more familiar subtleties of the RNS approach.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)NSFUniv Estadual Paulista, UNESP, Inst Fis Teor, ICTP South Amer Inst Fundamental Res, BR-01140070 Sao Paulo, BrazilInst Adv Study, Sch Nat Sci, Princeton, NJ 08540 USAUniv Estadual Paulista, UNESP, Inst Fis Teor, ICTP South Amer Inst Fundamental Res, BR-01140070 Sao Paulo, BrazilCNPq: 300256/94-9FAPESP: 09/50639-2FAPESP: 11/11973-4NSFPHY-1314311