The first issue is that it takes forever for Extension Manager CC to check for the availability of updates for our extension. A minute or more.
The second more important issue is that once Extension Manager recognizes that an update is available, and I press Update, there is an error:
"An unexpected error occurred during download."
Going to the update url specified in the extension MXI file shows the appropriately formatted xml containing the download url.
The problem has been solved. The root cause is HTTP redirect.