  We consider non-perturbative terms in the 4d effective action due to BPS
D-brane instantons, and study their continuity properties in moduli space as
instantons cross lines of BPS stability, potentially becoming non-BPS. We argue
that BPS instantons contributing to the superpotential cannot become non-BPS
anywhere in moduli space, since they cannot account for the required four
goldstino fermion zero modes. At most they can reach lines of threshold
stability, where they split into mutually BPS multi-instantons, as already
discussed in the literature. On the other hand, instantons with additional
fermion zero modes, contributing to multi-fermion F-terms, can indeed cross
genuine lines of marginal stability, beyond which they lead to non-BPS systems.
The non-BPS instanton generates an operator which is a D-term locally in moduli
space, but not globally. This is due to a cohomological obstruction localized
on the BPS locus, where the D-term must be written as an F-term, thus ensuring
the continuity of the 4d contribution to the effective action. We also point
out an interesting relation between lifting of fermion zero modes on instantons
and 4d supersymmetry breaking.
