  N-body simulations that follow only a collisionless dark matter component
have failed to produce galaxy halos or substructure within dense environments.
We investigate the `over-merging' problem analytically and with numerical
simulations, by calculating dissolution timescales of halos due to physical and
artificial dynamical effects. The numerical resolution that has recently been
attained is such that mass-loss from two-body relaxation is negligible. We
demonstrate that substructure is destroyed in present simulations as a result
of large force softening combined with the heating sources of tides and
encounters with dissolving substructure. In the limit of infinite numerical
resolution, whether or not individual halos or substructure can survive depends
sensitively on their inner density profiles. Singular isothermal halos will
always survive at some level, however, if halos form with large core radii then
the over-merging problem will always exist within dissipationless N-body
simulations. In this latter case a dissipational component can increase the
halos central density enabling galaxies to survive.
