The metrics table in the database is keyed on the load_id which is the filename which was loaded.
Here is a general description of the expected process:
Moving files from the “archive” folder back to the “stage” folder will reprocess the files, and will not duplicate counts, so long and the filenames remain unchanged. (A long and the “load_id” matches in the metrics table, the existing data will be overwritten by the new data.)
You should not expect files to stay in the processing folder. This would probably indicate an error or timeout which prevents that file from completing processing and may prevent future processing. Details of an error such as this should be available in your webserver error log, or in the scheduledTaskLogs.