A fraction of individuals infected with SARS-CoV-2 experienced rebounds when treated with effective antivirals such as Nirmatrelvir/Ritonavir (Paxlovid). Although this phenomenon has been studied from biological and statistical perspectives, the underlying dynamical mechanism is not yet fully understood. In this work, we characterize the dynamic behavior of a target-cell model to explain post-treatment rebounds from the perspective of set-theoretic stability analysis. Without relying on the effects of the adaptive immune system or the resistance through viral mutations, we develop mathematical conditions for antiviral treatments to avoid viral rebound. Simulation results illustrate the critical role of dosage (i.e., the doses and timing of administration) in taking advantage of highly effective drugs and tailoring therapies.