Well in that case I've got no idea what the problem is... so I'd recommend Marty's suggestion of using an alternative to FSO, which could be like this:
Code:
Public Sub AutoWriteDispData()

Dim strThisTime As String
Dim intFileNum As Integer

On Error GoTo FileError:

   ' write file with time date stamp unique name
   strThisTime = Format(Now, "mm_dd_yyyy_____Hh_mm_ss")
   
   intFileNum = FreeFile
   Open "C:\CES\XRF_Control\Data_Files\" & strThisTime & ".txt" For Output As #intFileNum
   Print #intFileNum, gblstrAcquisitionFileData
   Close #intFileNum
   
   intFileNum = FreeFile
   Open "C:\SPCData\SPC_Data.txt" For Output As #intFileNum
   Print #intFileNum, gblstrAcquisitionFileData
   Close #intFileNum

Exit Sub
FileError:
MsgBox " FATAL ERROR WRITING DATA FILES !  " & " Error Description = " & Err.Description & "   Error Number = " & _
Err.Number
'(removed Err.Clear, as it doesn't do anything useful in cases like this)
Close #intFileNum 'this is safe in an error handler, as it will be ignored if the file number is not open

End Sub
Note that due to the keywords For Output the files will be replaced each time. If you want to add to the end of the SPC_Data file instead of replacing it, change For Output to For Append