Whatever the software team did seems to have resolved the issue after the latest updates (of Samsung Gear on Android OS I believe). My watch connects to my phone automatically all the time now via Bluetooth.
What software version do you have. I have an ATT S3 with Tizen 184.108.40.206 and I still have this problem. Yesterday I had to do factory reset 3 times to get it to connect to bluetooth on the phone. On reconnect, it would leave the LT in place and connect to headphone. Of course that did not work.
Do I have a different problem?
I've been doing some tests for the last month and at least for now the problem is gone; every time I get near the phone (oneplus 5) it will connect in 2 minutes. I really don't know if it's TASKER or Samsung work it out, and francly I'm not going to turn TASKER off. For me, nor connecting it's enough to sell the S3