I had the same problem. I even got a replacement phone but that didn't solve the issue. It was still losing 4G connection.
I think I fixed the problem by setting up a smart action on the Razr Maxx to turn off the background sync (action) when display is on (trigger). When I do this, the Google servers (indicated by blue 4G LTE and blue bars) are now disconnected (because 4G LTE and bars are now white) and now the phone works great -- no lost connection anymore! When the display times out and screen goes dark, then background sync starts up again and my email etc. gets retrieved and sent (i.e. the Google server connection is restored). I've operated this way for two days now and have not had the connection issue.
However, when you use Google Play to install new apps, it asks you to temporarily turn background sync back on, so you might encounter a "no connection" during the app installation (wait for connection to be restored, or switch airplane mode on and off to restore), but after new app installtion just turn the display back off and then on again, and the background sync will be turned off again when you use the phone.