Here is another option...

Code:
Private Sub BuildLogFile2()
'This uses a Temp File to save log info
'and then appends the temp file to the new log file.
    
    Dim strFile1 As String
    Dim strFile2 As String
    Dim strTemp As String
    Dim intNum1 As Integer
    Dim intNum2 As Integer
    
    
    strFile1 = "C:\My Documents\MyFile.log"
    strFile2 = "C:\My Documents\~MyFileLog.bak"
    
    'Do Clean up before processing
    'Use Resume Next in case file doesn't exists
    On Error Resume Next
    Kill strFile2
    
    'Now use Error Handler Routine
    On Error GoTo errHandler
    
    intNum1 = FreeFile
    
    'Back Up the Log File (Just to be safe)
    Name strFile1 As strFile2
    
    'Create New Log File
    Open strFile1 For Output As intNum1
    Print #intNum1, "New Line " & Now
    Close intNum1
    DoEvents
    
    'Append Old Log File to New Log File
    Open strFile1 For Append As intNum1
    intNum2 = FreeFile
    Open strFile2 For Input As intNum2
    Do Until EOF(intNum2)
        Line Input #intNum2, strTemp
        Print #intNum1, strTemp
    Loop
    Close intNum2
    Close intNum1
    
    'Clean Up
    Kill strFile2
    Exit Sub
    
errHandler:
    'An Error occurred so set things back the way they were
    Close intNum2
    Close intNum1
    Kill strFile1
    Name strFile2 As strFile1
    MsgBox Err.Description, vbOKOnly, "Error " & Err.Number
End Sub