There are following possible explanations:
- Make sure Brown Out Reset is disabled for your chip.
- Check your MCLR pin connections. It should have the following circuit:
simulate this circuit – Schematic created using CircuitLab
The exact values of of R1, R2 and C1 will vary as per your chip (consult the datasheet's reset section for that). But more or less this circuit acts as a low pass filter, thereby small disturbances in the power-line does not resets your PIC.
- After the 14V supply and 3.3V supply add large decoupling capacitors (of the order of ~50 uF or more). Also add 33 (or 22) pF capacitors along side large capacitors. The large one acts as 'local' charge reservoirs, so any small variations in the input side does not directly effect your digital supply. The large one acts as high pass filter. The little (33 or 22 pF) ones act as high pass filters suppressing any high frequency noise.
- You said you have decoupling capacitors on the PIC power input. That's good. But what are the values?
Please provide more information regarding your circuit diagram and your configuration bits and i will update my answer accordingly.