In robust video steganography, a message is embedded into a video such that video distortions are avoided while producing a stego video of imperceptible difference from the cover video. Traditional techniques achieved robustness against particular distortions but are complicated in computation and design, and rely on different compression standards. Nowadays, deep-learning-based methods can achieve impressive visual quality and robustness to attacks. We propose a framework with a channel-space attention mechanism for robust video steganography. The framework is composed of depthwise separable convolution layers that can learn channel-space segments for embedding and extraction. The secret messages are distributed across channel-space scales to increase imperceptibility and robustness to distortions. This end-to-end solution is trained with the 3-player game approach to conducting robust steganography, where three networks compete. Two of these handle embedding and extraction operations, while the third network simulates attacks and detection from a steganalyst as an adversarial network. Comparative results versus recent research show that our method is more robust against compression and video distortion attacks. Peak signal-to-noise ratio and structural similarity index were used for evaluating visual quality and demonstrate the imperceptibility of our method.