  Working to all orders in dimensionally-regularized QCD, we study the
radiation of a photon whose energy is much lower than that of external partons,
but much larger than the masses of some quarks. We argue that the conventional
soft photon theorem receives corrections at leading power in the photon energy,
associated with soft virtual loops of massless fermions. These additive
corrections give an overall factor times the non-radiative amplitude that is
infrared finite and real to all orders in $\alpha_s$. Based on recent
calculations of the three-loop soft gluon current, we identify the lowest-order
three-loop correction.
