  We consider a two dimensional SU(N) gauge theory coupled to an adjoint
Majorana fermion, which is known to be supersymmetric for a particular value of
fermion mass. We investigate the `soft' supersymmetry breaking of the discrete
light cone quantization (DLCQ) of this theory. There are several DLCQ
formulations of this theory currently in the literature and they naively appear
to behave differently under `soft' supersymmetry breaking at finite resolution.
We show that all these formulations nevertheless yield identical bound state
masses in the decompactification limit of the light-like circle. Moreover, we
are able to show that the supersymmetry-inspired version of DLCQ (so called
`SDLCQ') provides the best rate of convergence of DLCQ bound state masses
towards the actual continuum values, except possibly near or at the critical
fermion mass. In this last case, we discuss improved extrapolation schemes that
must supplement the DLCQ algorithm in order to obtain correct continuum bound
state masses. Interestingly, when we truncate the Fock space to two particles,
the SDLCQ prescription presented here provides a scheme for improving the rate
of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired
SDLCQ prescription is applicable to theories without supersymmetry.
