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Then take it to Apple. My rebooting issues were solved by replacing the phone NOT by installing iOS 7.1.

My phone was replaced SEVERAL weeks ago and not one reboot since. In some cases, its hardware, some software, and sometimes both. Until you go to Apple, you won't know.
 
Thanks, 7.1 was supposed to fix the issue, but I guess I will be headed to the Apple Store, just didn't want to drive 2 hrs for something 7.1 was supposed to correct.
 
Thanks, 7.1 was supposed to fix the issue, but I guess I will be headed to the Apple Store, just didn't want to drive 2 hrs for something 7.1 was supposed to correct.

I'm assuming you've restored the phone without installing a backup afterwards, correct?
 
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