Looks like the credentials stored with the connection are incorrect or out of date.
So Tableau prompts you - you give it correct credentials, which last the whole session, but Tableau doesn't change the existing embedded connection, so next time you open the work book the same thing happens.
To fix this, you need to explicitly edit your connection, set correct credentials and save it.
There is also a possibility that you use some kind of built-in identification that relies on operating system, and it got out of sync.
What are you connecting to?
Thanks - you were right. No idea how this password was deleted though (I'm the only Tableau Desktop user). Things now seem to work fine.
Connecting to SQL Server 2008. No, we don't use SSO or anything like that.