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My car quits by itself once over 35 miles

My car: Mercury Mystique 2000; Motor changed. Mileage: 86900

Once over 35 miles, it quits by itself.

The whole car body shakes right before it quits. Right before it quits, no matter how hard I press gas, speed will just go down. Yet, I can crank it after 1 or 2 minutes. But the car will stop in 20-25 minutes again. I went to local Ford Dealer for help. Paid over $70, they did not find anything wrong on their computer. Please help.