This issue occurs when you use FeedBurner's stats tracking capabilities to track clickthroughs back to your site; this clickthrough option is selectable as a checkbox on the Analyze > FeedBurner Stats PRO setup form.
If the FeedBurner-created clickthrough links back to your original content items do not work, one highly likely cause for trouble is that there are <guid> elements associated with each item in the feed, and these elements are missing a critical attribute:
isPermaLink="false"
If this attribute is missing, the <guid> element's own content is used as a permalink back to the original item, and this link almost never works. In most cases, the element value isn't a proper web address, so the redirected link fails.
By adding the isPermaLink attribute to your original feed's XML template as shown, FeedBurner will know to look in the <link> element for the URL to rewrite and ignore the <guid>.