  Cachazo and Strominger recently proposed an extension of the soft-graviton
theorem found by Weinberg. In addition, they proved the validity of their
extension at tree level. This was motivated by a Virasoro symmetry of the
gravity S-matrix related to BMS symmetry. As shown long ago by Weinberg, the
leading behavior is not corrected by loops. In contrast, we show that with the
standard definition of soft limits in dimensional regularization, the
subleading behavior is anomalous and modified by loop effects. We argue that
there are no new types of corrections to the first subleading behavior beyond
one loop and to the second subleading behavior beyond two loops. To facilitate
our investigation, we introduce a new momentum-conservation prescription for
defining the subleading terms of the soft limit. We discuss the loop-level
subleading soft behavior of gauge-theory amplitudes before turning to gravity
amplitudes.
