My Datasource model is automatically changed from composite to live model.

Hi Anonymous , 

You only seeing the second option doesnt mean your report that was published in Power BI Service itself has now been converted to a live connection. My report that is a composite model shows both options. Even my reports that are connecting in import mode show both options as well. Its just giving you an option to download the report that will have a live connection with the dataset should you choose to do so.

Full explanation (taken from https://learn.microsoft.com/en-us/power-bi/create-reports/service-export-to-pbix#limitations-when-downloading-a-dataset-pbix-file😞

• A copy of the report with a live connection to the data online. Choosing this mode results in downloading a .pbix file that contains the report you're downloading, but no data. Instead, the .pbix has a live connection to the dataset in the Power BI service. This mode is especially useful in situations in which Power BI Desktop would be unable to open the .pbix file if the data was included, such as for reports based on a dataset that is configured for large models or incremental refresh, or reports that have been modified by using the XMLA endpoint.

Now, the reason you cant see the first option which is prob what you are after is likely due to some other limitation. If you hover over the greyed part, what tooltip do you see? You should get some explanation as to why its greyed out. 

For more info on the two downloading options and their limitations, read here: https://learn.microsoft.com/en-us/power-bi/create-reports/service-export-to-pbix#limitations-when-downloading-a-dataset-pbix-file