I remember this issue did not occur in OS X El Capitan; only in macOS Sierra.
I guess I have go back to El Capitan and BitTorrent Sync 1.4.75 in order to do not have this issue again.
I have exactly the same problem. It causes a ridiculously fast battery drain to my MacBook Air Early 2015 running macOs Sierra 10.12.6 with Resilio Sync 2.5.7.