I have found that the Arduino Ethernet Shield has an issue where there is a power drop once it is plugged into the main Arduino unit. The voltage drop is due to the fact that power is fed from the Arduino to the Ethernet Shield through the cascading pins that the two devices share. To solve this problem I have switched out the battery pack that I was using with a larger 12 volt one that seems to have enough power to keep the Arduino and the Ethernet Shield both working. Hopefully this will be enough for now to power everything because the Arduino is also connected to a motor controller and a relay shield. The motor controller and the relay shield both have options for adding an external power source so perhaps I will need to power them separately from the Ethernet shield and the Arduino.