  We study supersymmetric AdS$_7$ vacua of massive type IIA string theory,
which were argued to describe the near-horizon limit of NS5/D6/D8-brane
intersections and to be holographically dual to 6D $(1,0)$ theories. We show,
for the case without D8-brane charges, that such vacua do not admit any
supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$
theories do not have a conformal manifold, thus extending previously known
results for supersymmetric deformations. It is also in line with the recent
conjecture that non-supersymmetric AdS vacua are in the swampland.
