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This is caused by a valve on the fuel tank. When you put fuel in the tank the air has to displace to allow room for fuel. This valve is where the air goes, it allows the air/fuel vapors into the evaporative emissions system. This is called on board vapor recovery. This way fuel vapors aren't allowed into the atmosphere, the canister stores the vapor remnants from the air and it is burned in the engine.
What is happening is this valve is allowing liquid fuel up into the evaporative emissions system and the vapor canister. A few minutes after you start the engine the purge solenoid comes on and pulls vapors from the system into the intake and burns them. When this liquid fuel is in the lines and canister it causes the engine to run very rich when the purge solenoid comes on, so it will run poorly or die when you are off the throttle.
There are two things that you can do. The permanent fix is to replace the fuel tank. The valving and hard plastic lines are part of the fuel tank. The other option is to not fill the tank up all the way. The fuel is pushing into the evap system when the tank gets full to the top. If you don't fill it all the way up this problem won't happen.