Networks that produce persistent firing in response to novel input patterns are thought to be important in working memory and other information storage functions. One possible mechanism for maintaining persistent firing is dendritic voltage bistability in which the depolarized state depends on the voltage dependence of the NMDA conductance at recurrent synapses. In previous models, the hyperpolarized state is dependent on voltage-independent conductances, including GABA(A). The interplay of these conductances leads to bistability, but its robustness is limited by the fact that the conductance ratio must be within a narrow range. The GABA(B) component of inhibitory transmission was not considered in previous analyses. Here, we show that the voltage dependence of the inwardly rectifying potassium (KIR) conductance activated by GABA(B) receptors adds substantial robustness to network simulations of bistability and the persistent firing that it underlies. The hyperpolarized state is robust because, at hyperpolarized potentials, the GABA(B)/KIR conductance is high and the NMDA conductance is low; the depolarized state is robust because, at depolarized potentials, the NMDA conductance is high and the GABA(B)/KIR conductance is low. Our results suggest that this complementary voltage dependence of GABA(B)/KIR and NMDA conductances makes them a “perfect couple” for producing voltage bistability.