We demonstrate the phenomenon of resonant activation in a nonadiabatically driven dissipative optical lattice with broken time symmetry. The resonant activation results in a resonance as a function of the driving frequency in the current of atoms through the periodic potential. We demonstrate that the resonance is produced by the interplay between deterministic driving and fluctuations, and we also show that by changing the frequency of the driving it is possible to control the direction of the diffusion.