Battery fast discharging
a 3S pack at 12000mAh means that the batteries should be able to supply 12A for an hour,

As the drivers are only rated for 4A per output, you would then expect it to run for about 1.5 Hours under full load - what ever the rest of the system is drawing for your use case

I fail to see why you would think larger motors would resolve this

If the battery pack voltage is really falling below about 7V (minimum rated voltage for the driver chips), then you have a bad connection or a really poor battery pack,

Another thing that might be going wrong is the large current spike when you start or stop the motor could be coupling a large amount of noise into the supply of what is controlling the drivers (the arduino), I would recommend making sure the motor power wiring is separate from the arduino supply wiring