My final solution thanks to your input. Items added or modified by the program are now saved to the database.

Code:
   Private Sub UpdateLeaderboard(ByVal jName As String, jWins As Integer)
        Dim test As Boolean = False
        'Check whether the name already exists
        Dim jRow As DataRow = SsrDataSet.JockeyLeaderboard.NewRow
        For XX = 0 To JockeyLeaderboardDataGridView.RowCount - 2
            If jName = JockeyLeaderboardDataGridView.Rows(XX).Cells(1).Value.ToString Then
                jWins = JockeyLeaderboardDataGridView.Rows(XX).Cells(2).Value
                test = True
                jWins += 1
                selRow = XX
                Exit For
            End If
        Next

        If test = True Then
            'update the record with new info
            jWins += 1
            Me.JockeyLeaderboardDataGridView.Rows(selRow).Cells(1).Value = jName
            Me.JockeyLeaderboardDataGridView.Rows(selRow).Cells(2).Value = jWins
        Else
            'the name is not present so add it
            Dim MyNewRow As DataRow
            MyNewRow = SsrDataSet.JockeyLeaderboard.NewRow
            With MyNewRow
                .Item(1) = jName
                .Item(2) = jWins
            End With
            SsrDataSet.JockeyLeaderboard.Rows.Add(MyNewRow)
        End If
        Try
            Me.Validate()
            Me.JockeyLeaderboardBindingSource.EndEdit()
            Me.JockeyLeaderboardTableAdapter.Update(Me.SsrDataSet.JockeyLeaderboard)
            'MsgBox("Update successful")
        Catch ex As Exception
            MsgBox(ex.ToString)
        End Try
        'just added to make sure it is reading the database
        Me.JockeyLeaderboardTableAdapter.Dispose()
        Me.JockeyLeaderboardTableAdapter.Fill(Me.SsrDataSet.JockeyLeaderboard)
    End Sub