During magnetic storms, relativistic electrons execute nearly circular orbits about the Earth and traverse a spatially confined zone within the duskside plasmapause where electromagnetic ion cyclotron (EMIC) waves are preferentially excited. We examine the mechanism of electron pitch-angle diffusion by gyroresonant interaction with EMIC waves as a cause of relativistic electron precipitation loss from the outer radiation belt. Detailed calculations are carried out of electron cyclotron resonant pitch-angle diffusion coefficients Dαα for EMIC waves in a multi-ion (H+, He+, O+) plasma. A simple functional form for Dαα is used, based on quasi-linear theory that is valid for parallel-propagating, small-amplitude electromagnetic waves of general spectral density. For typical observed EMIC wave amplitudes (1--10nT), the rates of resonant pitch-angle diffusion are close to the limit of strong diffusion, leading to intense electron precipitation. In order for gyroresonance to take place, electrons must possess a minimum kinetic energy Emin which depends on the value of the ratio (electron plasma frequency/electron gyrofrequency); Emin also depends on the properties of the EMIC wave spectrum and the ion composition. Geophysically interesting scattering, with Emin comparable to 1 MeV, can only occur in regions where (electron plasma frequency/electron gyrofrequency) ≥10, which typically occurs within the duskside plasmapause. Under such conditions, electrons with energy ≥1 MeV can be removed from the outer radiation belt by EMIC wave scattering during a magnetic storm over a time-scale of several hours to a day.