Connection problems with SQL Server in ASP.NET applications using out-of-process session state

I have several ASP.NET applications deployed in a farm of 4 Windows 2003 machines. Each application uses a separate App Pool and Virtual Directory in IIS. They rely heavily on sessions which are persisted out of process on a single SQL Server 2000 (<sessionstate mode="sqlserver" ... />). Applications are compiled against .NET 3.0 but .NET 3.5 SP1 is installed on servers.

Each web server receives approximately 10 requests/second. Every once in a while I get some exceptions in logs:

System.Data.SqlClient.SqlException: A transport-level error has occurred when receiving results from the server. (provider: TCP Provider, error: 0 - The semaphore timeout period has expired.)
   at System.Data.SqlClient.SqlConnection.OnError(SqlException exception, Boolean breakConnection)
   at System.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection)
   at System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj)
   at System.Data.SqlClient.TdsParserStateObject.ReadSniError(TdsParserStateObject stateObj, UInt32 error)
   at System.Data.SqlClient.TdsParserStateObject.ReadSni(DbAsyncResult asyncResult, TdsParserStateObject stateObj)
   at System.Data.SqlClient.TdsParserStateObject.ReadNetworkPacket()
   at System.Data.SqlClient.TdsParserStateObject.ReadBuffer()
   at System.Data.SqlClient.TdsParserStateObject.ReadByte()
   at System.Data.SqlClient.TdsParser.Run(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj)
   at System.Data.SqlClient.SqlCommand.FinishExecuteReader(SqlDataReader ds, RunBehavior runBehavior, String resetOptionsString)
   at System.Data.SqlClient.SqlCommand.RunExecuteReaderTds(CommandBehavior cmdBehavior, RunBehavior runBehavior, Boolean returnStream, Boolean async)
   at System.Data.SqlClient.S