If you are powering up the android box with an IR remote it is possible that the TV power command is the same as the MXQ power command so it turns the TV off (if it is already on). You can check this by using the MXQ remote to turn off the TV without the box connected to the TV.
If is also possible that the MXQ power command it the same as the TV off command. Even if your TV remote doesn't have separate on and off commands many manufacturers do have separate codes installed so that universal remotes have an easier time with macros. No simple way around this. Maybe just turn them on in the right order or use app to control the MXQ via wifi.
If it is not an IR problem the only other thing to try is to turn off the CEC function in the TV. This sends commands over the HDMI connection but doesn't work right much of the time especially with different brands.