Error 6 Overflow

Hi tekapo
You dont have a sheet called "Complaints Register - DS"

Hello tekapo,

Welcome to the Forum!

You keep recreating the Outlook Application. You only need to create the Outlook Application at the very beginning of the code.

Private Sub SendReminderButton_Click()
Dim OutlookApp As Object
Dim RowNo As Integer
RowNo = 4
Set OutlookApp = CreateObject("Outlook.Application")
Do Until Worksheets("SWR DS Complaints Register").Cells(RowNo, 1).Value = "" + Worksheets("SWR DS Complaints Register").Cells(RowNo, 2).Value = ""
    If Worksheets("SWR DS Complaints Register").Cells(RowNo, 13).Value = "Overdue" Then

        With OutlookApp.CreateItem(olMailItem)
          .Subject = "OVERDUE COMPLAINT: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 1).Value + Worksheets("SWR DS Complaints Register").Cells(RowNo, 2).Value
          .Body = "Regional Records indicate that the following Complaint from: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 4).Value & " regarding " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 8).Value & " is currently overdue. Please action accordingly and provide the Regional Coordinatation Team with an update as soon as possible."
          .To = Worksheets("SWR DS Complaints Register").Cells(RowNo, 16).Value
          .Send
        End With
    Else
      If Worksheets("SWR DS Complaints Register").Cells(RowNo, 13).Value = "On Schedule" Then
 
        With OutlookApp.CreateItem(olMailItem)
          .Subject = " OUTSTANDING COMPLAINT: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 1).Value + Worksheets("SWR DS Complaints Register").Cells(RowNo, 2).Value
          .Body = "Regional Records indicate that the following Complaint from: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 4).Value & " regarding " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 8).Value & " has not been completed. Please action accordingly and provide the Regional Coordinatation Team with an update as soon as possible."
          .To = Worksheets("SWR DS Complaints Register").Cells(RowNo, 16).Value
          .Send
        End With
    Else
        If Worksheets("SWR DS Complaints Register").Cells(RowNo, 13).Value = "Recommendations" Then

        With OutlookApp.CreateItem(olMailItem)
          .Subject = " OUTSTANDING RECOMMENDATIONS OF COMPLAINT: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 1).Value + Worksheets("SWR DS Complaints Register").Cells(RowNo, 2).Value
          .Body = "Regional Records indicate that the required recommendations of the Complaint from: " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 4).Value & " regarding " & Worksheets("SWR DS Complaints Register").Cells(RowNo, 8).Value & " have not been completed. Please action accordingly and provide the Regional Coordinatation Team with an update on the recommended improvement actions as soon as possible."
          .To = Worksheets("SWR DS Complaints Register").Cells(RowNo, 16).Value
          .Send
        End With
         End If
         End If
    End If
  RowNo = RowNo + 1
Loop
End Sub

Another point regards Overflow errors in general...

When storing Row numbers in Variables it is always advisable to use a Long Type variable given Row boundaries exceed those of the Integer type.

In VBA there's a general consensus that the Integer type is of very limited use given all Integers are in fact converted to Longs (and subsequently back to Integer) behind the scenes.
On that basis most would say - just use Longs
(or Byte if you know the value is going to be within Byte boundaries)

Integer is useful if you want to deliberately generate an Overflow Debug but I would say that's an unlikely scenario (given you can just sanity check the value of the Long)