First see what data source the report is using. In SSRS, when you have the report open go to Properties -> Data sources. Usually, you'll see a pathway to a shared data source (something like /Data Sources/Reporting DB). In the example I just used, from the Home menu you would go into the Data Sources folder and find a data source called Reporting DB. When you click on the data source, you'll see a properties screen that includes the connection credentials. If you know the current password for the user in the data source, re-enter it and click Apply.

Now try the report again and see if that fixed it. If not, the issue is probably something else.