  In a previous work, it was shown that all Ricci-flat spacetimes are exact
solutions for a large class of non-local gravitational theories. Here we prove
that, for a subclass of non-local theories, the Schwarzschild singularity is
stable under linear perturbations. Thus, non-locality may be not enough to cure
all the singularities of general relativity. Finally, we show that the
Schwarzschild solution can be generated by the gravitational collapse of a thin
shell of radiation.
