2004 Mercury Grand Marquis restarting itself

Sounds like the remote starter/security system going haywire . Tech over kill .

So, while driving, the engine shuts off, then it restarts itself while the car's still moving. I'm guessing this happens when the car is moving relatively fast. There are lots of causes for an engine to shut off, or die, while driving, and that can be related to electrical or fuel issues. And I think that's your problem. The engine restart occurs because the transmission is still engaged and it's spinning the engine fast enough when it recovers..... Have a mechanic diagnose this.