  The inspiral of stellar-mass compact objects, like neutron stars or
stellar-mass black holes, into supermassive black holes provides a wealth of
information about the strong gravitational-field regime via the emission of
gravitational waves. In order to detect and analyse these signals, accurate
waveform templates which include the effects of the compact object's
gravitational self-force are required. For computational efficiency, adiabatic
templates are often used. These accurately reproduce orbit-averaged
trajectories arising from the first-order self-force, but neglect other
effects, such as transient resonances, where the radial and poloidal
fundamental frequencies become commensurate. During such resonances the flux of
gravitational waves can be diminished or enhanced, leading to a shift in the
compact object's trajectory and the phase of the waveform. We present an
evolution scheme for studying the effects of transient resonances and apply
this to an astrophysically motivated population. We find that a large
proportion of systems encounter a low-order resonance in the later stages of
inspiral; however, the resulting effect on signal-to-noise recovery is small as
a consequence of the low eccentricity of the inspirals. Neglecting the effects
of transient resonances leads to a loss of 4% of detectable signals.
