There's no way the Roku can be powering down your entire system. Your player does have limited CEC support, which can send control signals through the HDMI cable to other devices. One of those commands can be for power. All of your devices would have to support the CEC protocols and accept a power off command from the Roku. Even on my sets that have a Roku remote with a power button, that power button only appears to be sending an IR signal to the TV. If I try to use the power button with the remote shielded from the TV, nothing happens.
But I have never seen any Roku player issue that command while an app is in use and playing a video. I suppose on a long shot chance there might be something defective in the box, that doesn't seem likely. It's more like something else in your HDMI chain might be signaling everything to turn off. My first suspect would be the cable box. Since it's not providing a signal to the system, it might be sending out a sleep command to the other devices.
Try playing something other than Netflix with the Roku, just to see if it continues to happen.