I read several threads and this seems the closest to the issue I am seeing. Not sure why some members say that others have jail broken their phone but it happened to me, as well.
I really didn't want to upgrade but clicked on OTA and thought nothing of it till it went into DFU mode. Then I knew all the info would be lost but I should have backed up first and/or never do OTA. But doing a manual upgrade did not fare any better since my iPhone 4 keeps rebooting.
Looking at the logs I saw a lot of Skype logs so I removed Skype. However the suggestion to "Reset" everything had a bit better results. Not using "FaceTime" gave a slight improvement (but I upgraded in hopes to renew the certificates).
FaceTime still does not work properly. It can receive and send out calls but fails to connect after confirmation.
Re-install and hard reset still leaves me with a race condition that causes the phone to reboot.
Seems that clicking the "wake" button or "wake" then "home" button can cause the phone to reboot. And the behavior seems to worsen with FaceTime and Skype. Not sure if I want to rip the phone apart to disconnect the battery, but have anyone seen this and have any suggestions?
Also why is it a hardware issue if the problem occurs after the upgrade?