Klinger RC
Is there a clue in the video?
When one motor cut out the other significantly speeded up suggesting that with both motors running the battery voltage is sagging badly. Add a servo current as well (particularly if the surface is not really free moving) and the battery voltage drops to a point where one of the ESCs hit its LVC as nerdic pointed out.
Do the controls continue to work when one motor has cut out? If an ESC has hit the LVC the servos should continue to work normally.
What capacity battery are you using and its C rating?
Do you know the current the motors are taking?
If you run the motors at very low power does a motor still cut out if you move a servo?
Can you test it with a bigger capacity battery to ensure the voltage does not sag.
This was my second thought. If he's using the AH set up as stated then he'll need a battery able to push about 20a. The battery seen in the video appears small and I'd be surprised if it was bigger than 500mah.