  The perturbative calculation of the lifetime of fermion excitations in a QED
plasma at high temperature is plagued with infrared divergences which are not
eliminated by the screening corrections. The physical processes responsible for
these divergences are the collisions involving the exchange of longwavelength,
quasistatic, magnetic photons, which are not screened by plasma effects. The
leading divergences can be resummed in a non-perturbative treatement based on a
generalization of the Bloch-Nordsieck model at finite temperature. The
resulting expression of the fermion propagator is free of infrared problems,
and exhibits a {\it non-exponential} damping at large times: $S_R(t)\sim
\exp\{-\alpha T t \ln\omega_pt\}$, where $\omega_p=eT/3$ is the plasma
frequency and $\alpha=e^2/4\pi$.
