My 2003 Buick la Sabre custom has cut out several times while driving.

While driving my 2003 La Sabre it cuts out. All electrical works. Seems as if gas isn't
making it to the engine. After hours of sitting it will start. Had it at the shop and the
mechanic said it runs and he cant find anything wrong with it. But he has has a few
people come in with the same problem. He doesn't want to put in a new fuel pump
because the car starts. Any one else have this problem and if so how did you resolve it?