Delete method of Range class failed (again)

When I run the following code, I get a Run-time Error '1004': Delete method of Range class failed. If there is nothing in column D, then the if statement is not satisfied and the macro runs fine and doesn't do anything.
Changing the Delete line to 'Rows(i).Delete Shift=x1Up' works just fine, but I would prefer to just delete the selected range.
Here is the entire macro:

Sub AssignRequests()
    Dim i As Integer
    i = 2
    Do While i <= Range("OutstandingCount") + 10
    If Range("D" & i) <> "" Then
    Range("PasteRange").Value = Range("A" & i, "D" & i).Value
    
       Range("A" & i, "D" & i).Delete Shift:=x1Up
    
    Else: i = i + 1
    End If
    Loop
End Sub

This is my first post, so I hope it is done correctly.
Thanks!