2002 Ford Focus Engine Stalling

I have Focus that has started doing this weird thing and seems that it only does it in the hotter summer months. And if its been running a long time. If I stop somewhere and shut it off for a short time and then come back and restart it, it will start but die as soon as it starts. It will start right back up, but die as soon as it does. If I give it gas as I start it, it will stay running but I have to keep the rpm's up or if I rev it up a few times it might be ok. I had a new Ford fuel pump put in so I was thinking it can't be that, but then again it could. I also noticed a couple times last week the motor done a very quick stumble while I was driving, kinda like if I could have shut off the switch and back on very fast. Hope someone can help, because if I had hair to pull out I would, its driving me crazy. Thanks