SQL Server Connection Client Tried To Connect To An Unsupported Version?

We recently launched a new web site.there are roughly ~150 users active during peak hours.During peak hours,we are experiencing an issue every few minutes,the exception text is listed below.

System.Web.HttpUnhandledException:
Exception of type 'System.Web.HttpUnhandledException' was thrown.
---> System.Data.SqlClient.SqlException: The client was unable to establish a connection because of an error during connection initialization process before login.

Possible causes include the following:
the client tried to connect to an unsupported version of SQL Server;
the server was too busy to accept new connections;
or there was a resource limitation (insufficient memory or maximum allowed connections) on the server.(provider: Named Pipes Provider, error: 0 - No process is on the other end of the pipe.)

Our data access layer calls various DataTableAdapters using the following syntax.

EDIT

Yes, da is the name assigned to the DataTableAdapter. There is no connection.Open() because the DataTableAdapter takes care of all that, right?

using(TheDataLayer.some.strongly.typedNameTableAdapters.suchAndSuchTableAdapter da

[code]...

The connection string looks something like:

<add name="MyConnectionString"
connectionString="Data Source=myDBServerName;Initial Catalog=MyDB;User ID=MyUserName;Password=MyPassword"
providerName="System.Data.SqlClient" />

I'm trying to rule the problem being in Code.Is there anything "simple" that can be done to minimize this issue?