Do you have Auto_Close enabled on your SQL Server properties?

That's the first thing I would check. If not, then I would get a network sniffer running while you try to establish the connection again. See if that tells you anything.

Other options are to do a tracert and a ping from the location of this particular Access db to see if that machine can even hit the SQL server.

EDIT: It's also giving an "Access Denied" in that error, so I'd check permissions too.