As a Zip user, I have the same "my Fitbit Zip has stopped synching" issue. I just experienced this problem, again, from 9pm last night until a few minutes ago. What I have found is that the battery is low even when the Zip shows it as being fully charged. There is sufficient battery charge to run the Fitbit but not enough to sync with my phone or PC. I replaced the battery with a new CR2025 and all is well (again).
I had last replaced the battery on 2/28/2019, so it was 2 months old. I tested the old battery and it registered 2.87V, which is low for a 3V battery.
Even taking the battery out and putting it back in may work for a time or two, but the problem is that the battery probably needs to be replaced.
