  Oscillons are localized states of scalar fields sustained by self
interactions. They decay by emitting classical radiation, but their lifetimes
are surprisingly large. We revisit the reasons behind their longevity, aiming
at how the shape of the scalar potential $V(\phi)$ determines the lifetime. The
corpuscular picture, where the oscillon is identified with a bound state of a
large number of field quanta, allows to understand lifetimes of order of $10^3$
cycles in generic potentials. At the non-perturbative level, two properties of
the scalar potential can substantially boost the lifetime: the flattening of
$V(\phi)$ and the positivity of $V''(\phi)$. These properties are realized in
the axion monodromy family of potentials. Moreover, this class of models
connects continuously with an exceptional potential that admits eternal
oscillon solutions. We check these results with a new fast-forward numerical
method that allows to evolve in time to stages that cannot be otherwise
simulated on a computer. The method exploits the attractor properties of the
oscillons and fully accounts for nonlinearities. We find lifetimes up to
$10^{14}$ cycles, but larger values are possible. Our work shows that oscillons
formed in the early Universe can be stable on cosmological time scales and thus
contribute to the abundance of (ultra)light scalar dark matter.
