Q: Cannot update iPhone 4 from iOS 7.0.4 to 7.0.6 update begins & then just stops & restarts device

I was experiencing this issue also.  To resolve it, I installed iTunes onto my laptop, and integrated my iPhone4 with iTunes.  iTunes saw the iOS was out of date at 7.0.4 and should be at 7.0.6 for the security patch to be effective.  This resolved my inability to directly update the iOS.

Use the steps in the section titled "Update your device using iTunes" in the following article:

Update your iPhone, iPad, or iPod touch

http://support.apple.com/kb/ht4623

My resolved help request: https://discussions.apple.com/message/24973946#24973946

Rogue-Dave