2001 Honda Accord car seems to hesitate only when fuel is a

Hello, the car runs fine until the fuel tank reaches half a tank then it begins to hesitate and almost die when trying to accelerate. If we fill the tank up it will hesitate upon acceleration for a few seconds then it runs fine. Please help. The dealership has replaced the fuel pressure regulator, distributor, ignition coil twice, done a complete carbon cleaning due to throttle sticking, power steering flush, and replaced almost the entire ignition system and computer. It has cost us over $2500. Any ideas? They are at a lost and want to keep the car for approximately 3 days to look at it.