Engine stop running during driving, doesn't start after

could be the fuel pump or plugged fuel filters.

fuel injector or pump relay may have over heated and bunt out they do over time then the magnet cannot move to switch the fuel on or the injectors to work. these are in the engine bay fuse box. also check the fuse in there to as this can blow when the relay goes.

Could be a number of things but may want to begin by checking wiring to starter, battery, or even the ignition switch. These components may not turn your engine light on.

run the scanner to reset the ECM and immobiliser
make sure that the cranking speed is fast
check for air in the system
check that the stop solenoid is connected

my car has the same exact problem!! i have 2 pop the clutch 2 get it started when it is hot. Mine starts great when its cold or hasn't ran 4 awhile but when we are driving around for more than about 20 min in it when we stop it doesn't start at all. it wont even turn over. so i have 2 have my husband push it while i pop the clutch & then it starts & runs fine till the next time we turn it off. its not a battery problem as we'v replaced the battery, & the starter & the alternater are fine as we'v had them tested. hopefully someone that knows & has fixed this problem can answer this mystery problem!! hopefully some1 can :D

Do an upper intake clean that will clean the throttle body and the Idle Air Control valve. Also clean the mass air flow sensor

If your loosing antifreeze and you keep driving your engine will stop running because it over heats and the engine seizes. You are lucky the heads arn't all warped and the engine ruined from overheating the oil and turning it into thick goop. Then the engine doesn't get oil and melts togeather

You have to separate engine issues, from transaxle
slippage
Could you tell us more info & detail

I assume it is automatic & the trans is gone,unless
you say it shifts fine & has serious engine problems
& no one so far has been able to resolve

What is the time frame here on all vehicle issues?

My first thought would be: If you repaired an emissions hose, take the car back to Auto Zone (or another parts supplier) and let them tell you what code comes up now. You eliminated one problem, now you have to find another.
I wouldn't do a fuel pump without more information.
Gary

Try Crank Position Sensor it is a known issue with the ML's. They breakdown and are very easily affected by heat.