On your development machine, the windows account you are logged on with has access to the SQL Server database.
On the server, the service account of theQlikView services is used to attempt access to the SQL Server database (still running with Windows security). Apparently, that account can't get in.
Generate a DocumentLog and it will show you the cause of this failure (Settings->Document Properties->General->Generate Log File)
Solution: In SQL Server, grant access to the target database to the service account.