The issue was that the base path which was used to generate the application ID, prefixed to the authentication information in the session, did not match on each server. Amazon OpsWorks was deploying the code to the servers using the identical symlinked path, but the real path returned by PHP differed due to versioning and symlinking.
For example, the symlink path on both servers was '/app/current'. However, the actual path on one server was '/app/releases/2014010700' and the other was '/app/releases/2014010701', which was generating a different hash and therefore not working with the session.
Changing the base path to use the symlink path in my configuration file fixed the problem, whereas before it was using dirname() which was returning the real path of the symlinked contents. I also had to remove the realpath() function in setBasePath in the Yii framework.
The modifications I made to the Yii framework are quite specific for my issue, but for anyone else experiencing a similar issue with multiple nodes, I would double check to ensure each node contains the application in the exact same path.
Thank you to the following article: http://www.yiiframework.com/forum/index.php/topic/19574-multi-server-authentication-failure-with-db-sessions