  We study a discretization of ${\cal N}=2$ super Yang-Mills theory which
possesses a single exact supersymmetry at non-zero lattice spacing. This
supersymmetry arises after a reformulation of the theory in terms of {\it
twisted} fields. In this paper we derive the action of the other twisted
supersymmetries on the component fields and study, using Monte Carlo
simulation, a series of corresponding Ward identities. Our results for SU(2)
and SU(3) support a restoration of these additional supersymmetries without
fine tuning in the infinite volume continuum limit. Additionally we present
evidence supporting a restoration of (twisted) rotational invariance in the
same limit. Finally we have examined the distribution of scalar field
eigenvalues and find evidence for power law tails extending out to large
eigenvalue. We argue that these tails indicate that the classical moduli space
does not survive in the quantum theory.
