After following all of the steps in the article http://support.apple.com/kb/TS1559, if the problem persists you have a hardware failure.
I forgot to ask if this is all networks or only your home network. If it is only your home network reboot your router by removing all power from it for about 15 seconds.
Message was edited by: Lawrence Finch
Settings > Airplane Mode ON and Do Not Disturb ON
Power down and wait 5-10 minutes
Settings > Airplane Mode OFF and Do Not Disturb OFF
If that does not help, backup the content, then reset to factory condition and then restore your backup.
If that does not help, try a visit to an Apple store genius bar for testing.
I'm absolutely certain it is happening to some iPhone 5's. Also iPhone 4S's, iPhone 4's, iPhone 3GS's, iPhone 3's, and original iPhones. But I don't see how this helps your decision. Things break. Even iPhones. If yours is broken get it replaced, and if the new one has the problem you can get IT replaced, ad infinitum.