When a backup job is completed successfully, Artifactory looks at the last modified date on each of your subfolders within the backup destination folder. The elapsed time from that time stamp to the current time is then calculated. If there are any backup folders with a calculated time that's longer than your system's configured retention period, the process will delete them.
However, if you configure your backup retention for 168 hours (7 days) and configure your build to run every week, your old backup might not get deleted when your new backup completes successfully. This will happen if the elapsed time calculation is less than 168 hours. To be certain whether or not this is happening to you, check your filesystem. If the last modified date on your previous backup folder is less than 168 hours from the timestamp on your latest backup, then this explains your problem.
Thus, to make sure that your backup is deleted every week, configure your retention period to a value that's reasonably lower than 168 hours (e.g., 160 hours).