  We analyse the classical stability of the model proposed by Maggiore and
Mancarella, where gravity is modified by a term $\sim m^2 R \Box^{-2} R$ to
produce the late-time acceleration of the expansion of the universe. Our study
takes into account all excitations of the metric that can potentially drive an
instability. There are some subtleties in identifying these modes, as a
non-local field theory contains dynamical fields which yet do not correspond to
degrees of freedom. Since some of them are ghost-like, we clarify the impact of
such modes on the stability of the solutions of interest that are the flat
space-time and cosmological solutions. We then find that flat space-time is
unstable under scalar perturbations, but the instability manifests itself only
at cosmological scales, i.e. out of the region of validity of this solution. It
is therefore the stability of the FLRW solution which is relevant there, in
which case the scalar perturbations are known to be well-behaved by numerical
studies. By finding the analytic solution for the late-time behaviour of the
scale factor, which leads to a big rip singularity, we argue that the linear
perturbations are bounded in the future because of the domination of Hubble
friction. In particular, this effect damps the scalar ghost perturbations which
were responsible for destabilizing Minkowski space-time. Thus, the model
remains phenomenologically viable.
