The Volterra-type Lyapunov functions are an ubiquitous tool for establishing global stability in systems appearing in mathematical biology. We show, however, that no function of this type can be a Lyapunov function for the endemic equilibria of a classical intra-host model of malaria-the AMG model. More precisely, we give a sharp condition on the model parameters for this to be the case. This condition leaves out a large and biologically meaningful parameter range that will have to be addressed by a different method. We also present a set of three alternative arguments that enlarge the range of parameters for which global stability can be obtained-including parameter ranges that are relevant to malaria.