What thickness of wire should be used to power Arduino on 9 meters?
Your servo is pulling too much power from your Arduino every time it moves, causing your Arduino to reset. You can use some smoothing capacitors to store some extra charge for quick use (although I've never tried this myself), or you can hook up an extra set of batteries/power adaptor for the servo.

Connect the +ve and -ve power from the extra batteries to your servo, and the -ve of the extra power to the -ve of your original power supply (so that the servo positioning signal from the Arduino can ground back to the original supply).

I have a photo of how I have this set up on my site, along with a description of how I set it all up.