  We study the retarded field sourced by a uniformly accelerated particle in a
non-local scalar field theory. While the presence of non-locality regularizes
the field at the location of the source, we also show that Lorentz-invariant
non-local field theories are particularly sensitive to the somewhat unphysical
assumption of uniform acceleration, leading to logarithmic divergences on the
acceleration horizon. Analytic properties of the non-local retarded Green
function indicate that the divergences can be removed by placing appropriate
sources on the acceleration horizon in the asymptotic past.
