The kind folks at Fitbit got back to me about my syncing issues and they were able to solve the problem.  I expected I’d be receiving a new Fitbit One, but instead they had me reset the tracker.  I haven’t seen this procedure in the documentation, so if you have a similar problem try this…

To restart your One tracker, please do the following:

1. Plug your tracker into the charging cable, which needs to be connected to your computer. Please make sure that the gold dots on your tracker align with the gold contacts in the inside of the charger. When you hear a click, you will know your One is in the charging cable properly. 

2. Hold down the button on your tracker for 12 seconds. 

3. Remove your tracker from the charging cable. 

4. Press the button on your tracker until the screen illuminates again. Your One should function properly now.