  Most models for asymmetric dark matter allow for dark matter self
annihilation processes, which can wash out the asymmetry at temperatures near
and below the dark matter mass. We study the coupled set of Boltzmann equations
for the symmetric and antisymmetric dark matter number densities, and derive
conditions applicable to a large class of models for the absence of a
significant wash-out of an asymmetry. These constraints are applied to various
existing scenarios. In the case of left- or right-handed sneutrinos, very large
electroweak gaugino masses, or very small mixing angles are required.
