Server timeout ved forbindelse til Oracle via C#

Ved forbindelse til Oracle via C# kode får jeg følgende fejl:

OracleTest.xslt System.InvalidOperationException: Timeout expired. The timeout period elapsed prior to obtaining a connection from the pool. This may have occurred because all pooled connections were in use and max pool size was reached. at System.Data.OracleClient.OracleConnectionPoolManager.GetPooledConnection(String encryptedConnectionString, OracleConnectionString options, Boolean& isInTransaction) at System.Data.OracleClient.OracleConnection.OpenInternal(OracleConnectionString parsedConnectionString, Object transact) at System.Data.OracleClient.OracleConnection.Open() at <sourcefile>

Min C# kode er som følger (jeg har fjernet SQL statement og connectionstring):

        public string OracleTest()
        {
            try
            {
                string resStr = "";
                int    lineNo = 0;
                string sqlString = "*******";

                OracleConnection conn = new OracleConnection( <connectionstring> );
                conn.Open();
                try
                {
                    OracleCommand cmd = conn.CreateCommand();
                    cmd.CommandText = sqlString;
                    OracleDataReader reader = cmd.ExecuteReader();
                    reader.Read();
                    return reader.GetOracleValue(0).ToString();
                }
                finally
                {
                    conn.Close();
                }
            }
            catch (Exception e)
            {
                return e.ToString();
            }
        }

Funktionen fejler allerede på conn.Open().

Hvad kan der være galt?