If you checked Save old gamelist in the Gamelist Options tab, ARRM will make a backup of your old gamelist, before saving the new one
You can force a backup of all your gamelist.xml by clicking on the Backup gamelists button in the Gamelist Options tab. A folder with the name of each system present will be created in the %appdata%\Nexouille soft\arrm\temp\backup folder which will contain the gamelist.xml backups in the form: gamelist_yyyymmdd-hhmm.xml example: gamelist_20211119-1955.xml
You can directly access the backups folder via the View Backup directory button on the Tools tab
Remember to clean up these directories from time to time.