PBI and Dataset issue

If the desktop refresh works, but the service does not, then it is most likely a permission issue with the gateway accessing the data. Except you said it was Project Online. How are you connecting? Is that a gateway data source? I don't see any connector in Power BI for that, so I don't know what the underlying source is.

I do know that if you are using any special code in the Advanced options area of a SQL Server connection your gateway must have higher than normal permissions to excecute the code, otherwise it works fine on the desktop and fails in the service. But I don't know enough about Project Online via Power BI and how that connection works. Just tossing this out there as being a permission issue that is a bit more trouble than "if it works on the desktop it should work on the service." 

Could you provide more specifics on the connector?