Further progress in the development of electron cyclotron resonance (ECR) ion sources (ECRISs) requires deeper understanding of the underlying physics. One of the topics that remains obscure, though being crucial for the performance of the ECRIS, is the electron energy distribution (EED). A well-developed technique of measuring the EED of electrons escaping axially from the magnetically confined plasma of an ECRIS was used for the study of the EED in an unstable mode of plasma confinement, i.e., in the presence of kinetic instabilities. The experimental data were recorded for pulsed and CW discharges with a room-temperature 14 GHz ECRIS at the JYFL accelerator laboratory. The measurements were focused on observing differences between the EED escaping from stable and unstable plasmas. It was found that nonlinear phenomena alter the EED noticeably. The electron losses are enhanced in both unstable regimes, with two-frequency heating suppressing the instabilities. It has been shown earlier that two-frequency heating boosts the ECRIS performance presumably owing to the suppression of instabilities. We report the observed changes in EED introduced by the secondary frequency in different regimes, including an off-resonance condition, where the secondary frequency is lower than the minimum frequency satisfying the resonance condition for cold electrons at the magnetic field minimum. Finally, we suggest an experimental method of qualitative evaluation of the energy distribution of electrons confined in the magnetic trap using a method of measuring energy distribution of lost electrons during the plasma decay in pulsed operation of the ion source.