As you know, I am the guinea pig here and I am migrating two sites from HTTP to HTTPS, this site and my corporate site. Both use Feedburner, which was acquired by Google in 2007, but there is constant fear that Google will kill off.
In any event, Google is encouraging all webmasters to switch to HTTPS but if Feedburner dos not support HTTPS source URLs, then those URLs must remain HTTP.
When I migrated those sites, I tried to update the source URL of my feed in Feedburner settings but Google's Feedburner did not like the URL and spit back at "Received HTTP error code 400 while fetching source feed" error.
Here is the process, I edit the feed sure by adding an HTTPS to the URL:
But when I hit save, I get this error:
So the only URLS on this site that are not HTTPS are my original source feed URLs that only Feedburner should have access to.
This is something all sites need to consider when migrating to HTTPS, if they use Feedburner.
Forum discussion at Google+.