The first thing I would look at is your crankshaft position sensor.  This is
a common failure item and often displays the same symptoms.

Does the engine runs rough before cutoff or just instant shutoff?

Sounds like an electronics issue. Semiconductors will often become
"open" when heated when they are defective and once they cool down
function normally again. I don't know the E430 but I have seen this in
electronic ignition components in a variety of makes and models. When
the component heats up it just shuts the engine down as if you turned
the key.  It's can be a hassle to find too since the component may
test normally by the time you check it.