Прекратите использование нескольких подпрограмм события Worksheet_Change и переключитесь на один Workbook_Sheetchange в листе частного кода ThisWorkbook.
Option Explicit
Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
Select Case LCase(Sh.Name)
Case "sheet1", "sheet2", "sheet3"
If Not Intersect(Target, Sh.Range("A:Z")) Is Nothing Then
On Error GoTo exit_out
Application.EnableEvents = False
Dim rw As Long, t As Range
For Each t In Intersect(Target, Sh.Range("A:Z"))
With Worksheets("Log")
rw = Worksheets("Log").Range("A" & Rows.Count).End(xlUp).Row + 1
.Cells(rw, "A") = t.Address(0, 0)
.Cells(rw, "B") = Environ("UserName")
.Cells(rw, "C") = Now
.Cells(rw, "D") = t.Value
.Cells(rw, "E") = Sh.Name
End With
Next t
End If
Case "log"
'do nothing
End Select
exit_out:
Application.EnableEvents = True
End Sub