The persistence of human immunodeficiency virus type-1 (HIV-1) has long been attributed to its high mutation rate and the capacity of its resulting heterogeneous virus populations to evade host immune responses and antiviral drugs. However, this view is incomplete because it does not explain how the virus persists in light of the adverse effects mutations in the viral genome and variations in host functions can potentially have on viral functions and growth. Here we show that the resilience of HIV-1 can be credited, at least in part, to a robust response to perturbations that emerges as an intrinsic property of its intracellular development. Specifically, robustness in HIV-1 arises through the coupling of two feedback loops: a Rev-mediated negative feedback and a Tat-mediated positive feedback. By employing a mechanistic kinetic model for its growth we found that HIV-1 buffers the effects of many potentially detrimental variations in essential viral and cellular functions, including the binding of Rev to mRNA; the level of rev mRNA in the pool of fully spliced mRNA; the splicing of mRNA; the Rev-mediated nuclear export of incompletely-spliced mRNAs; and the nuclear import of Tat and Rev. The virus did not, however, perform robustly to perturbations in all functions. Notably, HIV-1 tended to amplify rather than buffer adverse effects of variations in the interaction of Tat with viral mRNA. This result shows how targeting therapeutics against molecular components of the viral positive-feedback loop open new possibilities and potential in the effective treatment of HIV-1.