is the battery not suffiecient enough power supply?
Very likely. Those 9v batteries are an invention of the devil, good only for very low power devices like smoke detectors and that is about it. It has been said that the reason why Tandy went out of business was that all their stuff used 9v, and their real business was selling 9v batteries to suckers - who eventually woke up to the scam.
Your situation is not helped by the ethernet shield being a bit of a power hog.
I don't know what the best solution is for battery power, it obviously depends on the duty required. I imagine 7.2v of AA NiMH 1800 mAH would be a good and obvious place to start, as they can provide a good slug of power to prove you are going in the right direction.