This Python 2.7 or 3.x compatible script will watch a directory and move DaVinci Resolve DRP files to a backup folder one level below.
When a Resolve user repeatedly saves DRPs using a keyboard shortcut they will overwrite each other because they all use the same file name. When the script is running it will append the original name with a timestamp and move the DRP file to the backup directory.
Only tested in Linux, but it should work on all three supported OS-es. Windows does not come with Python. You need to install it yourself.
The best way to run the script is from the command line because it will report progress. That way you can also easily stop it with CTRL+C.
Make sure to start the script before you save any DRPs. At start the script will delete any lose files it finds in the watched folder.
You can also run this script from Resolve script dropdown menu and see the reporting in the Resolve built in console.