We present calculated elastic differential cross sections for positron-acetylene scattering, obtained by using the Schwinger multichannel method. Our results are in very good agreement with quasielastic experimental data of Kauppila et al. [Nucl. Instrum. Meth. Phys. Res. B $192,$ 162 (2002)]. We also discuss the existence of a virtual state (zero-energy resonance) in ${e}^{+}\ensuremath{-}{\mathrm{C}}_{2}{\mathrm{H}}_{2}$ collisions, based on the behavior of the integral cross section and of the s-wave phase shift. As expected the fixed-nuclei cross section and annihilation parameter ${(Z}_{\mathrm{eff}})$ present the same energy dependence at very low impact energies. As the virtual state energy approaches zero, the magnitude of both cross section and ${Z}_{\mathrm{eff}}$ are extremely enhanced (at zero impact energy). The possibility of shifting from a low-lying virtual state to a shallow bound state is not expected to significantly affect room-temperature annihilation rates.