1988 Ford Thunderbird car won't start after driven a couple

I do have a mechanic and this has been an on going problem since 09/07. I drive to the grocery, then drive to a 2nd destination, car sits for alittle while, starts up then after letting it sit at the 3rd destination, the car won't start. It sounds like it wants to start up, but won't turn over for fear of draining the battery. After I let the car sit for a couple of hours, maybe more, it will start right up. I have taken the car to my mechanic, making his shop the last stop to get it to do this problem and suceeded, he put a pressure gage to check fuel pressure and it was @ 0 when attempted to start the car. He didn't think it was the fuel pump since he said the car wouldn't start it the pump was bad. He replaced the spark plug module and both the relay switches behind the radio. Fuel and EEC-IV? Switches a week ago Friday and it is still doing the same thing. I can't afford for him to keep guessing what it is but do appreciate his efforts and honesty. Can you help?