From the shutdown mailbag:

Hi Joe,

As we announced earlier this year, we’re making several upcoming changes to support FeedBurner’s next chapter. Here’s what you can expect to change and what you can do now to ensure you’re prepared.

Now starting in mid August, we are transitioning FeedBurner onto a more stable, modern infrastructure. This will keep the product up and running for all users, but it also means that we will be turning down most non-core feed management features, including email subscriptions, at that time.
For those who use FeedBurner email subscriptions, we recommend downloading your email subscribers so that you can migrate to a new email subscription service.

For many users, no action is required. All existing feeds will continue to serve uninterrupted, and you can continue to create new accounts and burn new feeds. Core feed management functionality will continue to be supported, such as the ability to change the URL, source feed, title, and podcast metadata of your feed, along with basic analytics.

Learn More

Thank you,

The FeedBurner team