Traditional DB singleton connection works poorly

I am using singleton database connection inside my java application, here is code of my connection manager class:

public abstract class DatabaseManager {
    //Static instance of connection, only one will ever exist
        private static Connection connection = null;    
        private static String dbName="SNfinal";
        //Returns single instance of connection
        public static Connection getConnection(){       
            //If instance has not been created yet, create it
            if(DatabaseManager.connection == null){
                initConnection();
            }
            return DatabaseManager.connection;
        }   
        //Gets JDBC connection instance
        private static void initConnection(){           
            try{        
                Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");
                   String connectionUrl = "jdbc:sqlserver://localhost:1433;" +
                      "databaseName="+dbName+";integratedSecurity=true";

                DatabaseManager.connection =
                             DriverManager.getConnection(connectionUrl);        
            }
            catch (ClassNotFoundException e){       
                System.out.println(e.getMessage());
                System.exit(0);
            }
            catch (SQLException e){         
                System.out.println(e.getMessage());
                System.exit(0);
            }
            catch (Exception e){        
            }       
        }
    public static ResultSet executeQuery(String SQL, String dbName)
    {
        ResultSet rset = null ;
        try {
               Statement st = DatabaseManager.getConnection().createStatement(ResultSet.TYPE_SCROLL_INSENSITIVE,ResultSet.CONCUR_READ_ONLY);
               rset = st.executeQuery(SQL);
               //st.close();
        }
        catch (SQLException e) {
            System.out.println(e.getMessage());
            System.exit(0);
        }
        return rset;
     }

    public static void executeUpdate(String SQL, String dbName)
    {
        try {
               Statement st = DatabaseManager.getConnection().createStatement();
               st.executeUpdate(SQL);
               st.close();
        }

        catch (SQLException e) {
            System.out.println(e.getMessage());
            System.exit(0);
        }
     }
}

The problem is my code work perfect at the start but when time past it becomes really slow. What caused that problem and how can i fix that? At starting time my application handles around 20 queries per second, after 1 hour of running it reaches to 10 queries per second and after 3 days of running it reaches to 1 query per 10 seconds!! P.S: My application is a single user application that makes many queries through database. P.S: Here is my JVM parameters in eclipse.ini:

--launcher.XXMaxPermSize
512M
-showsplash
org.eclipse.platform
--launcher.XXMaxPermSize
512m
--launcher.defaultAction
openFile
--launcher.appendVmargs
-vmargs
-Dosgi.requiredJavaVersion=1.6
-Xms500m
-Xmx4G
-XX:MaxHeapSize=4500m

Unfortunately database is remote and I have not any monitoring access to it for finding out what is going on there.

Here is the example of my usage:

String count="select count(*) as counter from TSN";
ResultSet rscount=DatabaseManager.executeQuery(count, "SNfinal");
if(rscount.next()) {
    numberofNodes=rscount.getInt("counter");
}