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Yes, it is possible that the new fuel pump is bad. Many times they will have an intermittent problem and work for a while and then stop, only to keep repeating the process. If I was working on the car and had an doubts about the pump, I would install a fuel pressure gage on it in such a manner that you could monitor it from the drivers seat. Maybe duct tape it to the windshield wiper arm or something similar. Then you could drive the car and when it acts up you could look at the gage and see if the pressure had gone away or not. It might not look good, but sometimes you have to go to extra lengths, just to get a good diagnosis done. You could do the same thing with the ignition system. Connect a volt meter to the main power leads going to the coil pack or module and connect it so you can see the meter when driving. Then if the voltage goes away when the car acts up, you know it is an ignition problem. Once you know for sure if it is a fuel or ignition problem, than you know where to spend your diagnostic time and what parts need to be tested. Some of the ignition parts, like the coil packs and modules can be tested off of the car with the proper equipment. But when you get one that only acts up sometimes, it can be a lot more difficult to find the problem. Sometimes something as silly as a loose ground wire or bad connection in the system, can drive you nuts trying to find it. Have them give some of these things a try and see if it doesn't help isolate the problem. You could also buy a spray can of starting fluid and a screw driver, to keep it in the car and the next time it acts up just spray a shot of the starting fluid into the intake and see if that makes it start right up. If so, that would be a pretty good indication of a fuel delivery problem. If it makes no change, then suspect ignition problems. The big trick to fixing it, is going to be to get it to act up when it can be tested. Thanks