The reason your xbox is rebooting is because Microsoft put in a loopback in the RCA connection, so if an interruption in the HDMI handshaking process occurs, the xbox will reboot.
This can be counteracted by placing tape over two specific pins on the composite connection cable.
This is completely free, and can be achieved by using nothing but the composite cable your 360 S came with, and an HDMI cable.
That motherfucker right there is what's responsible for your trouble. It's the loopback pins. Now you can easily take this pin out of the picture by placing tape over it as shown in the next image.
Those two pins right there are the ones you want to be sure to get. Covering up other pins can cause things to not work.
That's it. All you have to do now is connect it, and you're in business.
