The stability of fermionic charge carriers on cosmic strings is considered. We show that neutral fermion currents in cosmic strings are always chiral or time-like, in contrast to the case of bosonic currents. The spectrum of bound states on an abelian SO(10) string is determined both before and after the electroweak phase transition. We determine the mass acquired by the zero mode at this transition. A range of charge carrier scattering processes are considered and corresponding decay rates calculated. Couplings between the carriers and the electroweak sector generate scattering from the plasma which can thermalise some currents. If the zero mode is isolated from the electroweak sector, then it survives. Current-current scattering is considered, but found to be unimportant in realistic settings where the string density is low.

RevTex, 28 pages, 3 figures