  Transient orbital resonances have recently been identified as potentially
important to the inspiral of small bodies into large black holes. These
resonances occur as the inspiral evolves through moments in which two
fundamental orbital frequencies, $\Omega_\theta$ and $\Omega_r$, are in a small
integer ratio to one another. Previous work has demonstrated that a binary's
parameters are "kicked" each time the inspiral passes through a resonance,
changing the orbit's characteristics relative to a model that neglects resonant
effects. In this paper, we use exact Kerr geodesics coupled to an accurate but
approximate model of inspiral to survey orbital parameter space and estimate
how commonly one encounters long-lived orbital resonances. We find that the
most important resonances last for a few hundred orbital cycles at mass ratio
$10^{-6}$, and that resonances are almost certain to occur during the time that
a large mass ratio binary would be a target of gravitational-wave observations.
Resonances appear to be ubiquitous in large mass ratio inspiral, and to last
long enough that they are likely to affect binary evolution in observationally
important ways.
