iPhone 5 -- Issue with wifi connectivity

Are you restoring the device from a backup of an older device? Have you tried wiping the device clean and starting from scratch? Even though I know you're testing on a factory restored device that should in theory be perfect. It's possible something may have gone wrong when the software was loaded on the device.

I know I've experienced issues like this on devices I've upgraded. Wiping the device clean again and starting from scratch (without restoring any backup data) was the only way I resolved the problems.

 

I had exactly the same problem when I updated my i4 to IOS6, so it's gotta be an IOS6 problem IMO.

I could only sort the problem by renaming my router since the 'forget this network' option had completely vanished from my iPhones WIFI options.

I since discovered that you can reset all network settings on the iPhone. Might be worth a try. It's under the 'reset' option in settings.

 

Wi-Fi

I have two iPhone 5's and they both have the same issue outside the house. My daughter with her wi-fi in her dorm, and me when I am traveling. Generally connecting to wi-fi at Hampton Inns (which is provided by AT&T). Each time the phone goes to sleep you have to reauthorize the phone on the network. I did not have this issue with previous phones (3GS and 4S).
It's a pain!