It was announced about a year and a half ago that we would be turning down email subscription services as part of moving FeedBurner into maintenance mode. We shifted the old FeedBurner onto the new tech stack a several weeks ago and as part of that effort the email subscription service was permanently turned down. However, you can still export all of your subscribers from FeedBurner by clicking on the overflow menu, the three vertical dots to the right of "Configure proxy" and then select "Export email subscriptions".
I don't have any official recommendation as to which service to switch over to for email subscriptions but some other popular email services such as MailChimp provide similar subscription services.
Hopefully this helps and we apologize for the inconvenience.