Don't rely on syncing to back up your Zotero library! Be sure to back up the files in your Zotero library just as you back up other important files.
To find where your Zotero data is stored, open Zotero's preferences, choose the "Advanced" tab, then choose the "Files and Folders" sub-tab. The location will be shown under "Data Directory Location." Make sure this location is part of your regular computer backups!