I had the exact same issue. The cause could be different but in my case, after trying several different things like changing the connection string on the Data Source setup, I found that this was the infamous 'double hop' issue (more info here).
To solve the problem, the following two options are available (as per one of the responses from the hyperlink):
Change the Report Server service to run under a domain user account, and register a SPN for the account.
Map Built-in accounts HTTP SPN to a Host SPN.
Using option 1, you need to select 'Windows' credentials instead of database credentials to overcome the double hop that happens while authentication.