Look around on this discussion board and you'll see that it's full of people experiencing the same issue and there hasn't been a peep from support in weeks. FitBit seems to be done with the Zip; it's no longer listed on their website and there's a message at the top of this board stating that it's no longer being monitored.
The only thing that you can do is remove and reinstall the battery. For most of us, that allows it to temporarily sync. It also puts undue wear on the parts and will likely shorten the life of the Zip significantly.
Ultimately, I think it's in everybody's best interest to find an alternative product by a different company.
