Feedburner has been broken, receiving no updates, for years now. The end is surely nigh.
I've been worried about this, ever since their acquisition. However, if they shutdown FeedBurner, there would be a LOT of broken links suddenly left on the web. Kind of like bit.ly or tinyurl suddenly disappearing. I imagine the public backlash from this makes it a bit more tricky for Google to drop FeedBurner, than it was to drop Reader.