Your ActiveSheet.Range("rng").End(xlUp).Offset(1, 0).PasteSpecial is quite tricky.  Especially in a loop. Try below code:
Option Explicit
Sub tblcopypast()
Dim Month As String
Dim tbl As ListObject
Dim iCt As Integer
Dim jCt As Integer
Dim lastrow As Integer
Dim targetRange As Range
Dim actRange As Range
    Set tbl = ActiveSheet.ListObjects("Table1")
    Month = ActiveSheet.Range("E1").Value
    lastrow = tbl.ListRows.Count
    jCt = 0
    Set actRange = ActiveCell
    Set targetRange = ActiveSheet.Range("rng").End(xlUp).Offset(1, 0)
    For iCt = 1 To lastrow
        If tbl.DataBodyRange(iCt, 2) = Month Then
            tbl.ListRows(iCt).Range.Copy
            targetRange.Offset(jCt, 0).PasteSpecial xlPasteValues
            jCt = jCt + 1
        End If
    Next
    actRange.Select
End Sub
Sub DefineSamples()
'sample data I used to review your code!
Dim cell As Range
    Range("M1") = "F1"
    Range("N1") = "F2"
    Range("O1") = "F3"
    Range("P1") = "F4"
    For Each cell In Range("M2:P12")
        cell.Value = Int(Rnd() * 100)
    Next cell
    Range("E1").Value = "Jan"
    Range("N3").Value = "Jan"
    Range("N5").Value = "Jan"
    Range("N7").Value = "Jan"
    Range("N9").Value = "Jan"
    Range("N10").Value = "Jan"
    Range("N11").Value = "Jan"
    On Error Resume Next
    ActiveSheet.ListObjects.Add(xlSrcRange, Range("$M$1:$P$12"), , xlYes).Name = "Table1"
    On Error GoTo 0
    Range("Table1").HorizontalAlignment = xlCenter
End Sub