The guage-fixing dependence of the damping rate of the QED and QCD fermionic excitations at high temperatures and long wavelengths is reexamined in detail using the effective leading-order perturbation expansion developed by Braaten and Pisarski. In contrast with what is expected from recent formal discussions, explicit calculations in covariant gauges yield a fermionic damping rate that is gauge parameter dependent. This result has general implications for gauge theories at nonzero temperature.