Sporadic Error Message - SQL Server does not exist or access denied

I periodically receive "SQL Server does not exist or access denied." denied errors with my website setup. Here is the setup:

Webserver - Windows Server 2003 Web Edition with SP2. Windows Firewall enabled to allow port 80, 443, 21 and RDP incoming.

SQL Server - Windows Server 2003 R2 Standard Edition with SQL Server 2005 Standard Edition. Windows Firewall enabled. Port 1433 allowed from office and webserver, RDP from anywhere.

Everything will be running fine until I get the "SQL Server does not exist or access denied", then some pages will display and some won't. Can last from 5 minutes to an hour depending on traffic. Most of the time it will clear itself up. Seems that it will start happening when traffic gets heavy, though neither machine is over 30% CPU. SQL Server buffer cache hit ratio is 99.8%.

Here is the connection string:

"Provider=sqloledb;" & _
           "Data Source=207.158.xx.xxx;" & _
           "Initial Catalog=DBName;Trusted_Connection=true;" & _
           "User ID=DBUser;" & _
           "Password=xxxxxxx"Start Free Trial