I often use tethering now that it's enabled on Softbank network in Japan. I normally use WIFI connection. The thing is, my iPhone 5 is usually hard to discover from my computer (Macbook Air). Normally when I turn on the tethering and wait around 10 seconds, it shows up in the available networks in the computer. But after closing the computer, doing something else, than later (minutes, hours or days), without having switched tethering off on the iPhone 5, I don't think I was ever able to discover the iPhone 5 from the computer, without switching tethering on/off on the iPhone 5. Sometimes even after discovery, the connection itself fails because of "timing out". It seems the tethering discovery with iPhone 5 is weak. Is this normal or an issue? Is the iPhone 5 faulty? (I know most/many iPhone 5 have really bad WIFI hardware and/or software. Maybe it's related.) iPhone 5 is at iOS 6.1 I believe.
You should verify which software level you're on. 6.1 isn't available to the public yet. iOS 6.0.2 specifically fixes a Wi-Fi bug (Apple doesn't say what the particular bug is, but it affects Wi-Fi). Check to make sure you're not on 6.0.1. If you are, upgrade to 6.0.2 and see if the problem is resolved.