Hi, I hope you are well!
My name is***** will see if I can help you with this.
In the absence of any codes and diagnostic information, I usually consider the crank position sensor failing when hot then restarting when cooled slightly, the fuel pump cutting out and the ignition coil cutting out.
How old is the crankshaft sensor, ignition coil and fuel pump, do you know if they have ever been done?
When it next cuts out and it won't start, look at the rev counter to see if it shows the engine is being cranked over - if it doesn't show any rpm on cranking but then when it does, the engine starts, this would help to support this theory.
The engine ecu uses the crank position sensor as it's main point of reference for many of it's functions, in the absence of a crank signal, the ecu would simply assume the engine is not running or was stalled and would not trigger a fault as it believes the engine is not turning.
This is opposed to say a camshaft sensor, the ecu would know the engine is turning from the crank sensor and therefore fault the camshaft sensor as it is not getting a signal.
I would expect a fault code or engine management light for most other sensor issues.
The fuel pump, if you can hear it priming when you turn the key, listen out for it also when it next refuses to start, same again, if you cant hear it but then when you can it starts again, this would support this theory.
If it comes to the ignition, sometimes there are resistance test that can be done to assess the coil and we could look at this if needed.
Is there anything else I can help with?
If I have helped, please rate 5 stars as this is how I get credit for my time and research, I am happy to keep this thread open once rated and 'await more details' as they happen.