First, try it again after logging into our site. Another client told us that worked for them — and it will work if the problem was with your account's permissions.
However, most usually than not, the problem is a long-standing issue in Joomla. The Download ID in the extension actually does nothing. When you visit the Control Panel we try to copy it over to Joomla's #__update_sites table for the update site record of our respective software. Joomla then copies it over to the #__updates record when it detects an update. To cut a long story short, Joomla can "lose" the download ID from the #__update_sites table or not copy it over correctly yo the #__updates table. This means that the Download ID is not sent when Joomla is trying to download the update. No Download ID means no download is possible and the update fails.
The easiest solution right now is to publish the Installer - Akeeba Backup and Installer - Admin Tools plugins. These will forcibly apply the missing Download ID to the update package download URL when Joomla tries to download an update. We have rewritten these plugins to only use very simply Joomla! core code so they can't break on a major update again.
Further to that, the next major version will be available for Joomla 4 only (don't worry; we will still support Joomla 3 for the life of Joomla 3.10 plus two months as we've done in the past major Joomla updates from 1.0 to 1.5, 1.5 to 1.6 and 2.5 to 3.0). Joomla 4 actually lets you edit the Download ID directly in the #__update_sites table and seems to be much more stable in the sense it doesn't seem to be prone to "losing" the Download ID as easily.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!