Do you have access to the particular source in back end database? I guess you don't have privileges to access the source anymore.
You can do one thing just execute a simple select statement in back end client on your connected source and check whether it giving you any result or not. If not then you need to your database administrator for the access. Let us know if this help.
It looks like you've used Integrated authentication for SQL Server, meaning that you're logging in using your Active Directory credentials. Is that the case? If so, I believe Tableau Server will also try to use integrated authentication. But it will not use your AD credentials--rather, it will use the AD credentials of Tableau Server's "Run As" account. In this case, you'd want to either:
1) Ensure that Tableau Servers's Run As account has the necessary access to the database.
2) Use a standard SQL Server user, then publish using that user instead of integrated authentication.
Taking another look, it looks like Tableau Server may be running as NT AUTHORITY\NETWORK SERVICE. This is not a member of Active Directory, but a standard local Windows account. So giving it access to a database server via integrated authentication is not an easy thing to do. You'll either need to change Tableau Server to use an AD "Run As" account, then use option 1 above or you'll need to use option 2.