Ribonucleic acids (RNAs) are conformationally flexible molecules that fold into three-dimensional structures and play an important role in different cellular processes as well as in the development of many diseases. RNA has therefore become an important target for developing novel therapeutic approaches. The biophysical processes underlying RNA function are often associated with rare structural transitions that play a key role in ligand recognition. In this work, we probe these rarely occurring transitions using nonequilibrium simulations by characterizing the dissociation of a ligand molecule from an HIV-1 viral RNA element. Specifically, we observed base-flipping rare events that are coupled with ligand binding/unbinding and also provided mechanistic details underlying these transitions.