Memory reconsolidation has been demonstrated in various tasks and species, suggesting it is a fundamental process. However, there are experimental parameters that can inhibit reconsolidation from occurring (boundary conditions). These conditions and their mechanisms remain poorly defined. Here, we characterize the ability of strong training to inhibit reconsolidation at the behavioral, systems and molecular levels. We demonstrate that strong memories in rats initially are resistant to reconsolidation, but after sufficient time will undergo reconsolidation, suggesting that boundary conditions can be transient. At the systems level, we show that the hippocampus is necessary for inhibiting reconsolidation in the amygdala. At the molecular level, we demonstrate that NR2B NMDA-receptor subunits which are critical for the induction of reconsolidation of auditory memories in the amygdala, are downregulated only under conditions when strong memories do not undergo reconsolidation. This suggests that one molecular mechanism for mediating boundary conditions is through downregulation of reconsolidation induction mechanisms.