Gear S2 losing number sync when phone and watch lose Bluetooth connectivity

First of all, I have spent much time with AT&T Tech Support on getting the watch and phone in synch to start with. I have a Samsung Galaxy S7 and a Samsung Gear S2 Sport. Whenever I walk off from my phone far enough for the Bluetooth signal to drop, the number sync drops as well. Every. Single. Time. The big selling point was the ability to leave my phone at home to go for a walk or run to the gym or the grocery store and still get calls and texts on the phone's number.

I have done the factory resets on the watch several times, which seems to be AT&T's standard troubleshooting step one.

Am I missing something? Do I just have to learn to live with this or should I just cancel the wireless service and use the watch in Bluetooth mode alone?