Here, in Canada, with Rogers LTE, I experience the same issue.
Seeing all the posts here suggest that is is not the carrier being the issue.
Working at home with the Wifi, I switch it off before leaving, and the LTE network is still active.
Randomly, I get connected to either the 3G or to the LTE servers, and the switching is not totally transparent. The ultimate cure is to reboot, which is just a work around that we should not have to use, hopefully.
Unfortunately, the implementation of switching between Wifi and G3/LTE network might poorly implemented into the new iPad, is is the first Apple LTE device, isn't?
Either it is a hardware problem or a lack of seamless Ip adress switching into IOS, the operating system. Let's hope that is the latter and that can be corrected with an IOS patch/upgrade. If it is a poorly conceived hardware, with so much components packed behind that marvelous Retina display, we are in trouble, my friends...
We will have to watch closely this thread to see if Apple will come out with a rabbit from their hat. I gave my ipad,2 to my sister as an Easter surprise, but will I regret my dearly beloved iPad 2? I placed a link on my desktop to come back to watch and monitor.
Let's admit that these issues ust be scrutinized closely... And the different situations where it happens fully inventoried. Good luck to us, all!