I'd suspect the PIC, oscillator and drive methods first.
To pwm from a PIC, you need to be very sure that SW or clock faults
result in a switch that is off and a program that can recover or
self-reset into a safe to run state.
Check the drive, at the gate, and look for well defined drive voltage
levels.
The PIC outputs can go Hi-Z, if I'm not mistaken, so perhaps a smaller
pull down resistor is in order, to avoid long glitches at supply
turn-on.
If the mosfet is any distance from the PIC, a local drive buffer might
be advisable at the gate.
RL
Once the PWM module is enabled, it should only output 0V/Vdd unless
it's disabled in software or reset. It's conceivable that the WDT
could be resetting the chip and thus tristating the output, but even
making generous assumptions, I'm not sure that ~half a joule
worst-case is all that bad, unless it was happening very frequently.
What's the case temperature on the MOSFET in normal operation?
If it's running @50% duty cycle, 6A average, the power dissipation
could be in the 20W neighborhood without even considering the
switching losses.