IIS SQL connection fails under heavy load; reset IIS fixes temporarily

Server 1: SQL Server 2008 Standard Edition Server 2: Windows 2008 Server R2, IIS 7.0

A web-site on Server 2 requires data in SQL Server on Server 1.

Everything works fine for a while (weeks sometimes). Then, under heavy load, Server 2 reports it cannot connect SQL Server on Server 1. Once IIS on Server 2 reports it cannot connect to SQL on Server 1, it does not get better until IIS on Server 2 is restarted. Perhaps restarting the application pool would work as well as a full IIS reset. I'm not certain.

I've tried changing the connection string to increase the connection pool size to unreasonably large values (1,000). The failures still happen.

The web-site is written in C#. The data access layer is NHibernate.

Here is the start of the exception:

[SqlException (0x80131904): A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server)]
   System.Data.ProviderBase.DbConnectionPool.GetConnection(DbConnection owningObject) +428
   System.Data.ProviderBase.DbConnectionFactory.GetConnection(DbConnection owningConnection) +65
   System.Data.ProviderBase.DbConnectionClosed.OpenConnection(DbConnection outerConnection, DbConnectionFactory connectionFactory) +117
   System.Data.SqlClient.SqlConnection.Open() +122
   NHibernate.Connection.DriverConnectionProvider.GetConnection() +60
   NHibernate.Impl.SessionFactoryImpl.OpenConnection() +39

Any ideas why this is happening? How to diagnose/fix it? I'm frustrated and considering ripping out NHibernate, which will take months and probably lead to many other kinds of problems.

I think you have to increase connection timeout value and connection pooling as well. So that it won't release connection to SQL Server in heavy load.