If there was any kind of electrical surge/transient, it's possible the 
gate-source was damaged, though we'll never know for sure. MOSFETs can fail 
in the shorted (on) state, and that would also fry the coil. Automotive 
electrical environments are not well-behaved, and prone to transients when 
cranking the engine, or when the alternator kicks in/out.

The first thing I noticed is the 2 resistors really dont protect the 
gate-source from overstress (most-sensitive part of  MOSFET). You should 
put a zener diode between gate-and-source (anode to gate, cathode to 
source). I  think extra capacitance across gate-source will help because 
the MOSFET  has about 1500pF, which gives an RC time constant around 
1.5usec; that should be enough for the zener diode to conduct, but if you 
want to play it safe, add 0.1uF across gate/source.


Next, what does the pulse look-like ? In order for the MOSFET to be off, 
the input signal needs to close to the VDD supply value. Is that 12 volts 
since this is a vehicle ?
Per the datasheet, the MOSFET will start turning on if Vgs is -4 volts. So, 
if your supply voltage is +12V, the input must be at least +8V to keep the 
relay off.

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