Okay, so
the files are on the Kindle. Good.
As I said above, I believe the Kindle automatically stores old versions in some sort of Archived Editions sort filter or other (on the assumption that most people don't really want to clog up the view with ancient newspapers, maybe?). So check the UI options for that.
Unfortunately, I cannot be any more specific, as I don't really do periodicals and have no personal experience dealing with them.