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In the ThisWorkbook module of the workbook, paste the following code:

Private Sub Workbook_Open()
'Set StartTime when the workbook is opened.
    StartTime = Timer
'Schedule a call to CheckTime in the future to check elapsed idle time.
    Application.OnTime (Now + TimeValue(TimeCheckDelay)), "CheckTime"
End Sub

Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
'Something changed in the workbook, so reset StartTime.
    StartTime = Timer
End Sub

In A VBA code module in the same workbook, paste this code:

Global StartTime As Single

Global Const TimeLimitInMinutes = 58   'idle time threshold
Global Const TimeCheckDelay = "00:10:00"

Sub CheckTime()
    Dim NewTime As Single
'Get the time (seconds past midnight) now.
    NewTime = Timer
'If StartTime was yesterday, add 86400 seconds to NewTime.
    If NewTime < StartTime Then
        NewTime = NewTime + 86400
    End If
'If TimeLimitInMinutes has expired since StartTime was last
'updated, close the workbook without saving changes.
    If (NewTime - StartTime) > (TimeLimitInMinutes * 60) Then
        ThisWorkbook.Saved = True
        ThisWorkbook.Close SaveChanges:=False
    Else
'Otherwise, schedule a call to CheckTime in the future to check
'again later.
        Application.OnTime (Now + TimeValue(TimeCheckDelay)), "CheckTime"
    End If
End Sub