I'm having the same problem too! I went to the mall earlier where there is at least four or five bars of 4G (there's currently no LTE in my area), but my phone kept changing from 4G to Edge and no signal. It would do this a repeatedly and I thought my phone was broken (it might be), so I restarted my phone and I got the 4G back, but had less signal than I would usually get with my 4S. What's wrong with it?
P.S. I don't want to go back to Apple to get it replaced because I already had my first iPhone 5 replaced due to scuff marks!