iPhone 5 internet connection problems

I was wondering if anyone was having problems with the internet connection on their iPhone 5 and with LTE.

The LTE coverage is great when I have it, but if I happen to lose it, my phone will not have any internet connection. I have full bars and don't even get Edge or 3G showing up on the phone. The only way I get those back is to either A) power off/power on my phone or B) find a WiFi network to connect to. So usually this problem goes away when I go home and get access to WiFi, but it is annoying getting to work and getting LTE for a moment and then not having internet connection all day.

For reference, nothing has changed in the building I work in and this never happened with my iPhone 4S. With the 4S I only lost internet connection if I had no signal or very weak signal. But with full bars I always had great internet.

So has anyone else experienced this? Is this a bug with the iPhone not reverting to Edge/3G when LTE isn't available? Is this a bug with AT&T?