Some short-period, detached binary systems have recently been reported to experience very rapid orbital decay, much faster than is expected from the angular-momentum loss caused by gravitational radiation alone. As these systems contain fully convective stars, magnetic braking is not believed to be operative, making the large orbital-period derivative puzzling. Here we explore whether a resonant interaction between the binary and a surrounding circumbinary (CB) disk could account for the observed orbital decay. Our calculations indicate that the observed orbital-period derivatives in seven detached binaries can be produced by the resonant interaction between the binary and a CB disk if the latter has a mass in the range of $10^{-4}-10^{-2}~ M_{\odot}$, which is of the same order as the inferred disk mass ($\sim2.4\times 10^{-4}~ M_{\odot}$) in the post-common-envelope binary NN Ser.