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 .