Yahoo! recently made changes to the connection protocols in their Messenger service, which caused all sorts of problems with many instant messaging clients.
The quick fix for this is simple: in your client, change the server to which you connect to a fixed IP address that does not yet use the new connection protocol, such as 22.214.171.124. In Adium, this is done via Adium -> Preferences -> Accounts, clicking your Yahoo! account and then clicking Edit (or double-clicking the account), and changing the value for Login Server, as shown below:
The problem with this fix is that if and when Yahoo! and your client sync up in the future to fix this problem for good, the IP you’ve entered may not be optimal, so you’ll have to remember to go back at some point and change the Login Server setting back to its original value (scs.msg.yahoo.com), which is an alias for many Yahoo! Messenger servers.
Instead of making this change, Adium users can update to a new beta version (by clicking Adium -> Preferences -> General, and enabling “Update to beta versions when available“, and then Adium -> Check for updates) that seems to have included a fix to this problem.
In my case, since my work enviroment includes a reverse proxy, I also (for the first time) had to enable proxy settings for my connection to Yahoo! in order to get it working again.
I should mention that Adium’s development wiki claims that all beta versions of Adium include an Adium -> Debug Window feature, but this does not seem to be the case with the latest beta version (1.3.5rc1), which does not include such a menu item (unfortunately).