This will be on your SQL Server configuration side of things.  Make sure that you turn on TCP/IP services and support for each of the IPs (NICS) that provide access to the server.  I am willing to bet this is the step that you might have missed.  Once you can connect via TCP/IP then I am willing to be you can connect.

At any rate, this is a legitimate message coming from SQL Server, but my first guess to the issue you are fighting is as mentioned above.

We moved our developement databases from a server running sql 2005 to sql 2008.  When we try to setup a connection in the "Application Database Connections" from the StataFrame menu in vs, we select the new sql server but get a message "Invalid Server Connection - Could not authenticate the SQL server." when we click "Next".  We tried both integrated security as well as sql security.  We're able to connect to the new sql server via SQL Server Management Studio from the same workstation using either Integrated or SQL Security.  On a slightly side note, the Database dropdown that specifies the "StataFrame" database is never enabled.