Samsung Captivate :: Phone Randomly Shut Down Itself

Bought the Captivate on launch day. I had problems with the battery, phone restarting by itself, buttons at the bottom would not register when pushed. Took that Captivate back yesterday and exchanged it for a new one. The new one I got works much better. Little to no lag, buttons are working properly, and the battery is much better. Used it until about 3% of battery was left then put the charger in. Fully charged by midnight, unplugged it and went to sleep. Woke up this morning to find out the phone shut itself off last night. I woke up and tried to check my emails but the screen would not turn on. Held the power button and the phone turned on as if it was just starting it up. I bought my phone from a authorized AT&T reseller so I'm hoping they'll let me exchange it for another one again.

I called Samsung tech support but they weren't much of a help. They said I can send it in for repair or take it back to where I got it for another exchange. My phone is not rooted and not tampered with in anyway. I downloaded all the same apps for it which were only about 6 so far. The only new one I did download was one of those Sense Digital Clock ones and put the widget on my home screen. Other than that the phone is set up just like my previous one. I deleted the Sense Digital Clock app so maybe that was the culprit? I really do not want to take this one back again as the one shut down is the only problem. I'm going to wait a couple days to see what happens. My 30 days are up on the 17th so if it keeps on shutting down I'm taking this one back.