2003 Pontiac Sunfire sometimes hard to start, sometimes ok

My 2003 Pontiac Sunfire has 101,000 miles on it. Within the last 2 mos, my check engine light and trac control light started to come on intermittedly, but my car ran fine. We took it in to a service technician that stated the fuel injector needed servicing. We paid almost $140 for the service and for 2 weeks the lights stayed off. Then, all of a sudden, both lights came on again but this time stayed on, never going off at any point. We took it in again and this time when they hooked it up to diagnostic machine it said there was a fuel pump problem and the fuel pressure was considerably lower than it should be, I believe 35%. They were surprised at how much pep my car still had though when they took it on test drive. We were given estimate of $600 to replace fuel pump and decided to hold off until we noticed change in car performance. About a week after it was in shop for the second time, we about became stranded, car did not want to stay running after started and once car was push started it started right up again and ran fine. Some days, it starts like there's no problem at all and other days, it struggles to start but once it gets going, it's fine. We've had real hot and some cool days and there seems to be no correlation with outside temp, it's acted up in heat and cold. There's no problem with gas mileage, it gets 34 mpg. My husband believes the fuel pressure regulator could be problem and I've read the oxygen sensor could also cause this. The tech at the shop insists it's the fuel pump even though most people are stranded when that goes out?
Any advice would be greatly appreciated. We'd hate to drop $600 into the car when that may not be what's wrong.