I would start with the fuel . Change the filter and make sure you have no problems there . Leave it running or drive locally . Take a tool kit with you . When it cuts out , remove the fuel lines to check fuel is present . Be careful ,if there is fuel it will be under pressure , so protect your eyes . If all is ok , you may need to check the spray pattern in the injectors . This is obviously a bit more complicated . Next . Everything electrical from the ECU , down the the fueling and ignition system needs to be checked . I would unplug one at a time , spray them with electrical contact cleaner and plug back in , checking for corrosion and any faulty wires . I would also have a look at your ignition switch , alarm / immobiliser . Also when it cuts out , remove a lead and connect a spark plug and lay it on the block , you will then see if you have a spark on cut out . All you need for a car to run is a spark and fuel . So if both are present, it may point to a faulty immobiliser .
All the best , hope this helps .
Rob