What would cause a 81 cj5 jeep to sputter and then go dead after getting it up to 35 to 40 mph Runs fine in idle and in low speed Hard to start after it sputters out?

If the vehicle has a carburetor, check the rubber hose from the fuel filter to the carb. If it's old, when running at higher speed the increased pressure will cause the hose to "pinch" closed thus restricting gas flow.