In order for the workbook to have access to the entire database on the server side, the workbook will have to be published with the entire data source, not just an extract.
Like Tracy said, you need to publish the datasource when you publish your workbook. I can think of a couple of ways for you to still work with your dataset, but able to publish with the full source
When you connect to your actually database, would you be connecting live or use an extract?
If your database is fast enough to connect live, you can still work with a local extract, and right before you public, connect to your database, and replace the data source. Then publish your workbook.
If you are using an extract, one way I can see you work around it would be take an extract, and then schedule an incremental or full refresh after you publish your workbook.