If the admin is reviewing outstanding requests using the list functionality then he could simply add a boolean field (true/false) to the form labeled (for example) [archive].  Then filter the list output for only those records where the [archive] field value is not equal to 'true'.  The second he edited a record and checked the [archive] field, that record would disappear from the list.  Then to access those archived records in the future you could add an additional page (has to be on a different page) with a copy of the form/list (reference) where the list is either filtered only to show those records where the archive field equals 'True' or alternatively leave it unfiltered and it will show all records both flagged for archive and not.

The field should be a 'Restricted Form Field" so your end users cannot modify it you may also optionally wish to uncheck  "Display on List"since it will be obvious the status based on which page you are viewing.

Hope this helps.

If you are doing  testing it is helpful to run more than one browser (e.g. FF and Chrome, or IE) then you can have separate sessions at the same time and switch back and forth and refresh for previewing as different users,