Run-time error '1004': Delete method of Range class failed

I am trying to delete rows that DON'T contain certain names, the code I currently have is:

Function IsMember(v As Variant, vArray As Variant) As Boolean
    Dim vLoop As Variant
    For Each vLoop In vArray
        If v = vLoop Then
            IsMember = True
            Exit Function
        End If
    Next vLoop
End Function

Sub Delete_Conslt()
    Dim lLast As Long, i As Long
    Dim vConsultants As Variant
    lLast = Cells(Rows.Count, "H").End(xlUp).Row
    vConsultants = Array("John Smith", "Julian Den", "Nick Richard", "Helen Walk", _
        "Mark White", "Jed Walton", "Emma Sheppard", "Jill Long", "Nei Turner")
    For i = lLast To 1 Step -1
               If Not IsMember(Cells(i, "H"), vConsultants) Then
            Cells(i, "A").EntireRow.Delete
         End If
    Next i
End Sub

The issue is that when I run this code it gets to the end and succesfully deletes the unwanted rows but then comes up with an error :

Run-time error '1004': Delete method of Range class failed

If i choose to debug it highlights the following code:

Cells(i, "A").EntireRow.Delete

I can't work out what the problem is, if i remove the NOT from the code and make it delete the rows i wish to keep the code works perfectly fine.

If anyone has any ideas that would be great!!

Thanks for you help, but i dont really understand what you mean by a horizontal criteria list. Could you please explain a little more?