1995 Buick Lesabre car shuts down while running this is a d

Electrical problem
1995 Buick Lesabre 6 cyl Front Wheel Drive Automatic

This car was given to me had a mechanic look it over said everything was fine. On the way home, about two miles it died, with no warning. My boyfriend said it needed a tune up as it sat for a year. After tune up it would still die at random always starting right back up. Eventually the car stopped starting back up imediately, but now the fuel pump relay would be clicking very rapidly and while clicking the check enginelight will flicker on and off. As soon as the relay would stop clicking the car would start, sometimes having to wait 3 seconds to 15 minutes, random. We replaced the relay. The car did it again before we ever left the parking lot. My moms mechanic said it was either the ignition module or the fuel pump. We replaced both and that didn't fix it. Some confusing things are that at high speeds the car will try to die like there's no fuel if you catch at the right time and pump the pedal some times you can prevent it from dieing. When the gas gauge reads between half a tank and a quarter tank it almost never dies or sputters. It will do it hot or cold. This great free car has now cost me alot of money and I can't afford to be replacing things that aren't wrong with it please help.