We investigate the stability of dark solitons with respect to periodic amplification by studying sideband generation. It is shown that these sidebands grow exponentially as a result of a four-wave mixing process with the cw background. We derive expressions for the positions of the sidebands and present numerical simulations that are in excellent agreement with the theoretical description. A comparison is made with bright solitons, showing that dark soliton propagation is less perturbed only over very short amplifier chains. We also relate our results to laser cavities and discuss the prospects for dark soliton lasers.