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Go into wifi settings and select OTHER, and then manually type in your wifi network name and password. Don't select it from the list of networks. Lots of people have had the same issue, and for what ever reason, this fixes it.
 
IMO, a device should perform as expected.. if you have to do a workaround then there's obviously something wrong with it. As countless members have suggested, OP should take advantage of the warranty and get it replaced ASAP. she shouldn't worry about something not working correctly on the iphone. it should work just like how it should be bar none.
 
I have an Apple AEBS (one generation old) and some D-link access points to reinforce weak spots at opposite ends of my house. Every now and then, if I start software updating on my iPhone 5, I get "whatever app failed to load" with "retry" and "done" buttons. This only happens at home. If I'm in a hotspot away from home this almost never happens. To me this suggests there are STILL some intermittent wifi bugs with iOS 6.0.2. The only way to get Apple looking at this is to complain to AppleCare. You are in the free support period (90 days) so call them and worry the heck out of them about this, making sure to point out you have 2 identical devices one of which "just works" and one of which "never works".

Good luck!
 
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