Drug therapies against persistent human infections such as hepatitis C virus, hepatitis B virus, and HIV fail to consistently eradicate the infection from the host. Hence, recent emphasis has shifted to the study of antiviral therapy aimed at boosting specific immune responses. It was argued that structured therapy interruptions were required to achieve this, because such regimes have shown promising results in early HIV infection. Using mathematical models, we show that, contrary to this notion, a single phase of drug therapy can result in the establishment of sustained immunity. We present a simple relationship between timing of therapy and efficacy of the drugs required for success. In the presence of strong viral suppression, we show that therapy should be stopped relatively early, and that a longer duration of treatment leads to failure. On the other hand, in the presence of weaker viral suppression, stopping treatment too early is detrimental, and therapy has to be continued beyond a time threshold. We discuss our modeling results primarily in the context of HCV therapy during chronic infection. Although the therapy regimes explored here also have implications for HIV, virus-mediated destruction of specific immune cells renders success unlikely during the chronic phase of the infection.