Treatment of hepatitis C virus (HCV) is lengthy, expensive and fraught with side-effects, succeeding in only 50% of treated patients. In clinical settings, short-term treatment response (so-called sustained virological response (SVR)) is used to predict prolonged viral suppression. Although ordinary differential equation (ODE) models for within-host HCV infection have illuminated the mechanisms underlying treatment with interferon (IFN) and ribavirin (RBV), they have difficulty producing SVR without the introduction of an external extinction threshold. Here we show that bistability in an existing ODE model of HCV, which occurs when infected hepatocytes proliferate sufficiently faster than uninfected hepatocytes, can produce SVR without an external extinction threshold under biologically relevant conditions. The model can produce all clinically observed patient profiles for realistic parameter values; it can also be used to estimate the efficacy and/or duration of treatment that will ensure permanent cure for a particular patient.