All of you seem to suggest that the reset is caused by a power supply problem. I'm not sure this is the cause, specially as the reset does not happen when powering up the motor but after a while.
It seems more like the USB port is being reset. Could you check this out? Do you have a serial arduino to test it?
I've got some trouble myself with certain external power supplies causing the above mention USB port reset.
Just my two cents,
Miguel