VB运行Log文件问题

写了一段Log事件记录的程序，目的是每天创建一个以日期命名的文件，记录当天的运行信息，但是我下面的代码存在一个问题，就是如果重新启动软件，该Log文件会重新创建，当天之前的运行记录全部丢失，请问如何实现当天重新运行软件后，事件记录接之前的记录继续往下写？
代码如下：
Option Explicit
Public dtSaveLog As Date
Public Sub StatusUpdate(ByRef pMessage As String)
    Dim FileName As String
    Dim FileNumber As Integer
    Dim sMsg As String
    sMsg = Now & " --> " & pMessage
    WriteLine sMsg
    FileName = App.Path & "\LOG\" & Format(Now, "yyyymmdd") & ".LOG"
    FileNumber = FreeFile
    On Error GoTo ErrorHandler
    If (Now - dtSaveLog) > 7 Then
      Open FileName For Output Shared As FileNumber
      dtSaveLog = Now
    Else
      Open FileName For Append Shared As FileNumber
    End If
           
    Print #FileNumber, sMsg
    Close #FileNumber
Exit Sub
ErrorHandler:
    Close #FileNumber
    WriteLine Now & " > " & "Error = " & Err.Number & ", " & Err.Description <