We study the universal conditions for quantum nonperturbative stability against bubble nucleation for pertubatively stable AdS vacua based on positive energy theorems. We also compare our analysis with the preexisting ones in the literature carried out within the thin-wall approximation. The aforementioned criterion is then tested in two explicit examples describing massive type IIA string theory compactified on S3 and S3×S3, respectively. The AdS landscape of both classes of compactifications is known to consist of a set of isolated points. The main result is that all critical points respecting the Breitenlohner-Freedman (BF) bound also turn out be stable at a nonperturbative level. Finally, we speculate on the possible universal features that may be extracted from the above specific examples.