I think that the problem  is that when it sets up the for each sheet  it
identifies that there are, say 7 sheets. When it deletes one it does not
alter this number. so it eventually gets to a non-existent sheet.

Try doing it backwards

something like (untested code)

for x = worksheets.count to 1 step -1
With worksheets(x)
If IsDate(.Name) Then
If DateValue(.Name) <= DateValue(Date - 14) Then
Application.DisplayAlerts = False
.Delete
End If

End If


Next x

I can track down the problem  caused by
extensive recalculation whenever a sheet  is deleted.

Therefore, I have to turn off the automatic recalculation and turn it
on again  at the end.

Sub DeleteOld()

Application.Calculation = xlCalculationManual

For Each Sheet In Worksheets

If IsDate(Sheet.Name) Then
If DateValue(Sheet.Name) <= DateValue(Date - 14) Then
Application.DisplayAlerts = False
Sheet.Delete
End If

End If
Next

Application.Calculation = xlCalculationAutomatic

End Sub

No. It is not excessive calculation but trying to access a sheet  that does
not exist. To avoid this you have to process the sheets  from back to front
rather than from front to back