My guess is that this is a shared Access Database which then requires all ODBC DSN Names to be the same as well as connection properties for the linked tables. To explain further, I believe, if you link the tables using trusted connection then Access will "intelligently" attempt to open them again using the same type of connection.
The best bet would be to link the tables using the SQL Authentication rather than NT Authentication or Trusted connection. All subsequent connections to the tables linked in the Access database should attempt to use the SQL Authentication first and then logging in once should pass for all tables.
I hope that wasn't too confusing and I am not positive about the functionality being that way as I have not used Access in a while.
“He is no fool who gives what he cannot keep to gain that which he cannot lose” - Jim Elliot