In a fraction of SARS-CoV-2 infected individuals treated with the oral antiviral Paxlovid, the virus rebounds following treatment. The mechanism driving rebound is not understood. Here, we show that viral dynamic models based on the hypothesis that Paxlovid treatment near the time of symptom onset halts the depletion of target cells, but may not fully eliminate the virus, which can lead to viral rebound. We also show that the occurrence of viral rebound is sensitive to model parameters, and the time treatment is initiated, which may explain why only a fraction of individuals develop viral rebound. Finally, the models are used to test the therapeutic effects of two alternative treatment schemes. These findings also provide a possible explanation for rebounds following other antiviral treatments for SARS-CoV-2.