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Is the vehicle turning over when it cuts out?
Or do you turn the key and it does nothing?
Do the lights on the dash light up when turning the key?
It sounds like you may not be getting a good connection at the starter. Try this it has been known to fix this type of issue. Get a star washer which is a washer that has points around it so it digs in when you tighten it down. It needs to fit the main power cable stud on the starter. Remove the nut and take off the cable and install the washer in between the starter and the power cable and install the nut and tighten it down and see what happens. Below is what a star washer looks like just in case you havent seen one before.