Updated to new version, now all sites report a communications error. Verified that Remote Control has full permissions through firewall.
Documentation has not been updated to reflect any requirements needed for the Update Akeeba Backup function to work.
Attached log is representative of the error for all five domains I maintain.
UPDATE: I did not realize that the online documentation was not as current as the PDF file available at the Remote Control downloads page.
Problem was probably caused by having v3.2.5 of Akeeba Backup on my sites. Upgrades are now in progress.