None of the fixes above worked for me. Toggling data, airplane, etc. sometimes worked but more often than not I had to do a battery pull reboot. Problems always seemed to happen whenever I was changing from 4G to 3G areas, 3G to 4G areas, or even WiFi to 3G/4G.
Finally I just turned off 4G completely (choosing "CDMA Only" in network settings) and I've had no problems since. Definitely something buggy in the handoff when LTE mode is active. Turning it off fixed it, but now I have no 4G.
Though I'll take consistent 3G over frequent disconnects.