We investigate theoretically the switching behavior of a dithiolated phenylene-vinylene oligomer sandwiched between Au(111) electrodes using self-interaction corrected density-functional theory combined with the nonequilibrium Green's-function method for quantum transport. The molecule presents a configurational bistability, which can be exploited in constructing molecular memories, switches, and sensors. We find that protonation of the terminating thiol groups is at the origin of the change in conductance. H bonding at the thiol group weakens the S-Au bond and reduces by about one order of magnitude the transmission coefficient at the Fermi level, and thus the linear response conductance. Furthermore, protonation downshifts in energy the position of the highest occupied molecular orbital, so that the current of the protonated species is lower than that of the unprotonated one along the entire bias range investigated, from −1.5 to 1.5 V. A second protonation at the opposite thiol group has only minor effects and no further drastic reduction in transmission takes place. Our results allow us to re-interpret the experimental data originally attributing the conductance reduction to H dissociation.