Power BI not saving basic authentication credentials during scheduling

I think I was having the same issue you had here. My fix was very straight forward.

I went into Power BI desktop, editted the query for getting the data from the API to - Json.Document(Web.Contents("url"))

(No authorization headers included)

Set my credentials to Basic Auth and entered the credentials.

Saved and published the report up to the cloud.

When in the cloud version, I went to my dataset's settings and checked the "Data Source Credentials" to make sure everything was working.

Sure enough, I was faced with:

Your data source can't be refreshed because the credentials are invalid. Please update your credentials and try again.

BUT, there was a little spinning/loading thing next to the edit credentials link.

I decided to give it some time to see what would happen and boom!

Once it had loaded, the error went away and I could now set up my Scheduled Refresh.

Seems like the auth defaults to Anonymous until your basic auth has made the connection (seems to take a while the first time).

Not sure if this will help you but thought I'd post it anyway!