Maybe:

Sub onbeillp111zzaa()
Dim i As Long
Dim ws As Worksheet
Dim wb2 As Workbook
Set ws = Workbooks("Monthly_Report.xlsb").Sheets("ALL_FAILURES_1mon")
Set wb2 = Workbooks("Master_Fails_List.xlsx")
ws.Activate
For i = 2 To Range("A" & Rows.count).End(3)(1).Row
    Rows(i).Copy wb2.Sheets(Range("A" & i).Value).Range("A" & Rows.count).End(3)(2)
Next i
End Sub