When using a Database Connection which requires authentication via username and password, the authentication should be carried across all sessions of ArcGIS software which are using this database connection.
So if I connect to a database in ArcCatalog and complete the authentication, and then open an MXD in ArcMap which uses this connection, I should not have to authenticate again - ArcMap could check with ArcCatalog (and other instances of ArcGIS software) to confirm that the connection has already been authenicated, and then let me get on with my work rather than pester me for a username and password again.
