What battery? Link to data sheet.
What is the battery voltage?
Is there a voltage regulator between the battery and the PIC?
Are there caps connected close to the PIC?
How are these wired?
It is common to get a voltage drop on the wires and the battery when a heavy load is applied. It helps to run separate wires from the battery to the motor driver (of heavy gauge) and to the PIC. This way any voltage drop on the wire due to the high current draw from the motor (V = I*R) is not 'seen' on the wires to the PIC.