The kinship theory of genomic imprinting has explained parent-specific gene expression as the outcome of an evolutionary conflict between the two alleles at a diploid locus of an offspring over how much to demand from parents. Previous models have predicted that maternally derived (madumnal) alleles will be silent at demand-enhancing loci, while paternally derived (padumnal) alleles will be silent at demand-suppressing loci, but these models have not considered the evolution of trans-acting modifiers that are expressed in parents and influence imprinted expression in offspring. We show that such modifiers will sometimes be selected to reactivate the silent padumnal allele at a demand-suppressing locus but will not be selected to reactivate the silent madumnal allele at a demand-enhancing locus. Therefore, imprinting of demand-suppressing loci is predicted to be less evolutionarily stable than imprinting of demand-enhancing loci.