How do I run an arduino and a dc motor on a single battery pack?
The Arduino Nano V 3.0 has an LT1117 voltage regulator at VIN. The dropout is somewhere between ~1.1-1.5V. According to the Arduino tech spec. the lowest VIN should be 7 Volts, so you´re pushing the margins. What probably happens is that your unspecified motor pulls more current than the internal resistance of your circuit can handle, thereby dropping the voltage to the Arduino even more. You might get away with just adding one or two cells to the first setup. 

If you´re really using one of those batteryholders in the Fritzing picture, note that they can have quite high resistance.