Voltage drop after writing to slave register with I2C protocol
Your battery isnt capable of providing sufficient current to the motor phases.

AA cells are meant for low current operation - few hundred mA, and I haven't seen AA cells powering any power hungry devices like motors or pumps. 

Now to answer why the LED on the shield fades, I want you to take a look at the capacity-voltage characteristics (mAh - V curve) of the AA cell you are using. A cell, being a power source, can deliver power only up to some extent - Pmax. As the load current increases, the open circuit voltage of the cell drops until the load isn't removed. As the load is removed, the cell voltage rises to its open circuit voltage, OCV. (OCV level will decrease as the cell is aged/ used) . So a AA cell rated at 1.5v cell voltage, will obviously have less voltage across its terminals when connected to heavy loads. 

Now because your motor draws high current, the cell voltage will drop. As the circuit continues to operate, the energy stored in the cell decreases and hence the maximum deliverable power and hence the cell voltage. This justifies the fading of LED on the shield. As the cell voltage falls below the brownout level of the micro controller, the micro controller will turn off. 

Like you said, the shield turns ON after a while. This can be justified by the point I mentioned above - when load is removed, the OCV of the cell rises. When OCV becomes greater than the brownout level of the microcontroller, the MCU and hence the shield powers up!

Now, for the solution to this problem, I will recommend you switch to Li-ion cells. Stacking AA cells in parallel will only make the battery bulkier. Instead use 2 Li-ion cells connected in series. Generally, 18650 cells are rated at 2600mAh. Li-ion cells can give maximum of 2C A of current i.e 2x2600 mA = 5200mA in this case. That too for a size equal to 2 AA cells!