Support

TL;DR: This is a bug in Joomla!'s JUpdate cache. You can follow a 17 steps procedure, outlined below, to reset it.

Admin Tools does not fetch the Joomla! update information itself. Instead, it asks Joomla!'s JUpdate system to tell it if there is an update available and which version is the latest. This is the same Joomla! system also used in Extensions Managers for extension updates and in Joomla! Update for the Joomla! updates themselves. Like all update systems, JUpdate caches its results for a short period of time. Due to some bugs in that system, it is possible that the cache gets stuck for an indefinite period of time. In your case, a little over a year(!!!).

A possible solution is the following:

• Log in to your site's administrator back-end
• Go to Extensions, Extensions Manager
• Click on the Options button in the toolbar
• Click on the Preferences tab
• From the "Updates caching (in hours)" select 5
• Click on Save & Close
• Click the Update tab
• Click on the Purge Cache button
• Click on the Find Updates button
• Click on the Find Updates button for a second time (yes, I know, sounds crazy, trust me)
• Go to Components, Joomla! Update
• Click on the Options button
• From the "Update Server" drop down select Testing
• Click on Save & Close
• Click on the Options button again. IMPORTANT: You really do need to first click on Save & Close and THEN click on the Options button again!
• From the "Update Server" drop down select "Long Term Support (Recommended)"
• Click on Save & Close

At this point you should see the Joomla! Update component reporting "You already have the latest Joomla! version, 2.5.18".

You are now free to wonder why the "Refresh update information" button I had originally put in the Joomla! Update component was deemed "unnecessary" and had to be removed. Obviously, the 17 arcane steps above being carried out in the correct order, like a magic spell, are "more intuitive" than clicking a clearly labeled button, right? One of many Joomla!-related facepalms over the years. *sigh*

In any case, we have already identified it as a major source of confusion for Joomla! users. To this end we have created a new, free of charge, component called Akeeba CMS Update. It is still in alpha, but it tends to work much more stable than Joomla! itself. The trick is that we are not using any part of Joomla! to handle updates with this component. We have implemented our own code to retrieve update information, cache this information, download the update packages and install the updates. In an ironic twist, we made a better Joomla! update by circumventing Joomla! itself.