I have the very same problem.
My provider is Orange and I possess an Iphone 4 upgraded to iOS 6.0.1
When I share my connection through wifi, it starts working in the beginning then the connectivity goes "limited" and it stops working. For it to work again I have to reboot my iPhone.
The onset of the problem is very sporadic, sometimes it comes 5 mins after sometimes it can work for hours.
When I share my connection through the wire, it starts working as well then the connectivity also goes "limited" and it stops working. For it to work again I have to go to "Network settings" then Disable the local connection and then Enable it again.
This is pretty annoying when it happens a dozens of time over 4-5 hours.
NOTE :
- This NEVER EVER happened when it was working on iOS 5
- This happens WHICHEVER the provider is
- This happens whether the connection is USB or Wifi
Therefore the only conclusion is that iOS 6 is the culprit and this needs to be fixed.
I am waiting for a fix because this cannot go on, I cannot properly work with that.
While I was writing this message, the connection dropped again.
I tried resetting network settings but it failed to work.
Any guess?