Fuel pump
Had same scenario on one of our customer cars, Owner drove 100 miles, returned home, stopped outside garage, opened garage door to reverse in - car then stopped and wouldn't start again.
Next day started okay and drove 50 miles - returned home, got out to open garage door, put in reverse, car stopped wouldn't start again.
Following week tried car - started - went out for a drive, cut out whilst driving....recovered home on back of recovery truck....
Fuel pump had failed.
Replaced with the Walbro upgrade kit - started straight away and been fine since.