Originally Posted By: robricc
I don't really know what to make of this finding. Perhaps when on the LTE APN, the phone uses more juice and goes into some hibernation mode? There is no selection for that kind of behavior in CM that I can see, so hopefully this is tweaked over time.

This seems like a good theory. LTE as currently implemented is data only, and in most phones (can't find conformation on the S III) it's a completely different chip. The phone must remain on the 3G network for voice, but may only keep LTE active when it believes the user is actively using the device. It's likely something that needs to be tweaked in the custom rom to ensure proper fallback to 3G, including registering with the push servers what IP the device has. Or forcing LTE on all the time, which will likely result in a heavy battery drain due to two independent radios being up and running full time.