  In this work we examine the small mass limit of black holes, with and without
spin, in theories where a scalar field is non-minimally coupled to a
Gauss-Bonnet term. First, we provide an analytical example for a theory where a
static closed-form solution with a small mass limit is known, and later use
analytical and numerical techniques to explore this limit in standard
scalar-Gauss-Bonnet theories with dilatonic, linear and quadratic-exponential
couplings. In most cases studied here, we find an inner singularity that
overlaps with the event horizon of the static black hole as the small mass
limit is reached. Moreover, since solutions in this limit possess a
non-vanishing Hawking temperature, a naked singularity is expected to be
reached through evaporation, raising questions concerning the consistency of
these theories altogether. On the other hand, we provide for the first time in
this context an example of a coupling where the small mass limit is never
reached, thus preferred from the point of view of cosmic censorship. Finally,
we consider black holes with spin and numerically investigate how this changes
the picture, using these to place the tightest upper bounds to date on the
coupling constant for the dilatonic and linear theories, with
$\sqrt{\overline{\alpha}} < 1$ km.
