You could try running a VBScript file as a user logon script. Create the VBScript file (copy the contents below into notepad, then save the file with a .vbs extension)... then specify the file as a user logon script through Windows group policy.
Const OverwriteExisting = TRUE
Set objFSO = CreateObject("Scripting.FileSystemObject")
objFSO.CopyFile "C:\FSO\ScriptLog.txt" , "D:\Archive\", OverwriteExisting
obviously you edit the script to match your own setup. In the script above, "ScriptLog.txt" is the file you are copying and you're copying it to "D:\Archive"
To specify the script as a user logon script in Windows group policy, open the policy and enter it here... User Configuration\Scripts (Logon/Logoff)\Logon