Since you are referencing the SelectedItems directly as soon as one Item is removed the count is reduced and your loop does not execute on all items. Hence do the following
Private Sub button1_Click(ByVal sender As Object, ByVal e As EventArgs)
Dim count As Integer = listBox1.SelectedItems.Count
Dim selectedItems As List(Of String) = New List(Of String)
Dim i As Integer = 0
Do While (i < count)
selectedItems.Add(listBox1.SelectedItems(i).ToString)
i = (i + 1)
Loop
Dim i As Integer = 0
Do While (i < count)
listBox1.Items.Remove(selectedItems(i))
i = (i + 1)
Loop
End Sub