Two workarounds are available, a relatively easy one involving replacing a block of code in the functions.php file, with the other workaround being a bit more technical where you create a PHP script that “relays” the content of your feed to FeedBurner.
For most people, the block code replacement is likely to be the preferred route even though it involves diving into the PHP code. Luckily, you don’t have to do that as contributing WordPress developer Mark Jaquith has made available a patched functions.php file you can download and just replace the bugged one with.
[...] Note that this [bug] doesnâ€™t prevent FeedBurner (or anyone else) from fetching your feed 100% of the time. The issue only arises with certain RSS consumers and only on certain servers, and only when the feed attempts to return a 304 Not Modified header. So with FeedBurner, for instance, one fetch attempt may trigger it, but the next will be fine.
Although I’ve not seen any FeedBurner errors since I upgraded this blog to 2.0.6 earlier today, I’ve applied Mark’s patch.
An embarrassing “oops” but speedy and positive steps taken by the developers. Expect WordPress version 2.0.7 at some point, hopefully soon.