90 Honda Accord stalls & shuts off when braking or driving downhill (@ half tank or less of gas)

I own a 1990 Honda Accord. I was having trouble with fuel not getting to the engine. I originally had the fuel pump changed and it seemed to fix the problem. The problem recurred so I replaced the fuel pump myself and no luck. I took it to a mechanic; they changed the fuel filter, fixed some bare wires to the fuel pump, and changed the tube from the fuel pump to the fuel line. Then they charged me another $200 ($300 in total). They said that it was fixed but that I should keep the tank at least half full. That’s like the bad joke about the patient who says to his doctor “it hurts when I do this” and the doctor says “don’t do that”. Here’s what I’ve discovered so far:

  • The problem only appears when the car is at half a tank of gas or less.
  • The less gas (under half a tank) the worse the problem gets.
  • When I hit the brakes or drive downhill the car stalls and turns off.
  • When I drive in reverse or uphill it doesn’t stall and shut off.

I believe that there is something mechanical inside the tank that is not working right and that that is why when the car is not level or I hit the brakes (when the car is at half a tank or less) it stalls and shuts off. Any guesses?