Will crank but not start

Sometimes the car will not not run well. Cut off while I was driving, but it would usually cut right back on. Sometimes it would not start. It would crank but was not getting any gas so it would not start. Eventually it would always start. It did not happen often. Then for about three days it kept cutting off or hesitating when I tried to start it, not getting any gas. Then it just quit turning on. I got a brand new fuel pump and it seemed to fix it. Car was running great until a few hours later when it started hesitating to start, I had to rev the gas while cranking it. Next morning car would not start again. I do not understand. It has a new battery. Fuel filter is only a few months old. Fuel pump is brand new.