Thank you for the link.
I have tried to reproduce this behaviour with one of your episodes. I have add the URL to a post in one of my test blogs and started playing the episode to see whether or not the mechanism counts or not. It worked. I can see one download in my statistic tables - in the one of "Downloads Per Post" and "Downloads Per Media File".
I have modified the code of the statistic page for version 188.8.131.52. This solved a problem with media files which have white space in their file names. But it should not affect media files with file names which contain basically ASCII characters (and other web-save characters). If this recent modification would be the problem then the rows of your old files in this table would be affected by this too. Or have you changed the naming scheme of your podcast files?
I don't think they're being displayed on the "Downloads Per Media File" screen
Do I understand it right that you can not see the file names of the latest episodes in this table?
Or can you see the file names but the download numbers do not change?
Only to be sure: this "Downloads Per Media File" table has max. 25 rows. If you have more episodes with more than zero downloads then the files with the low download numbers are on the next page of this table. You can change the page by clicking on "Next Entries »" or by choosing the page with the select box which should be also visible in the table footer (if there are more than 25 rows).