Is it necessary for you to re-upload the file each time you edit it?
If you edit the file through the Google Drive web interface (drive.google.com) rather than on a local/desktop application, I don't believe it will alter the URL.
Do you have "Drive" installed as an application on your computer so that the files in your Google Drive show up in a local folder on your computer? When you edit files in that folder, it shouldn't require you to re-upload the file.
If you don't want to edit in Google Drive online or in the local Google Drive folder, perhaps your best bet is to edit in whatever local application you prefer, then copy and paste your changes into the Google Drive (online) version.