  Oscillons are extremely long-lived, spatially-localized field configurations
in real-valued scalar field theories that slowly lose energy via radiation of
scalar waves. Before their eventual demise, oscillons can pass through (one or
more) exceptionally stable field configurations where their decay rate is
highly suppressed. We provide an improved calculation of the non-trivial
behavior of the decay rates, and lifetimes of oscillons. In particular, our
calculation correctly captures the existence (or absence) of the exceptionally
long-lived states for large amplitude oscillons in a broad class of potentials,
including non-polynomial potentials that flatten at large field values. The key
underlying reason for the improved (by many orders of magnitude in some cases)
calculation is the systematic inclusion of a spacetime-dependent effective mass
term in the equation describing the radiation emitted by oscillons (in addition
to a source term). Our results for the exceptionally stable configurations,
decay rates, and lifetime of large amplitude oscillons (in some cases $\gtrsim
10^8$ oscillations) in such flattened potentials might be relevant for
cosmological applications.
