Those options you mentioned are not related to keeping locally deleted files. You didn't mention the product version or the type of backup you are running, so I'll just assume it's a File Backup on 6.x. If you're using a different backup or are using 7.0, then please clarify and, in addition, if you're on 7.0 let me know if you are using the new backup format.

Set the Retention Policy in the backup plan, rather than setting in Global Options. Uncheck the option for "Delete Files that have been Deleted Locally" and that should prevent any local files from ever being removed from backup storage. As an alternative, you can use the option with the delay to prevent those locally deleted files from being removed, for say 90 days.