The past few days I've been bringing in my new WIFI-only iPad and trying to use it tethered to my iPhone 5. It's been a frustrating experience so far. I've found that it works OK when the iPad is first tethered to the iPhone, but shortly thereafter the internet connection seems to drop out on the iPad, even though the iPhone is still reporting it to be connected OK.

The frustrating thing is that my Android device (Nexus 7) works well and stays connected to the internet when tethered to my iPhone.

Finally, in desperation, I did some experimentation today. Previously I was tethered over WIFI. I am now experimenting with turning off WIFI and tethering solely through Bluetooth. I also switched off the screen lock on my iPhone. So far this seems to have solved the disconnection issues I've been having.