K2 doesn't have (and doesn't need) an auto-archive feature. The "archive" feature was originally implemented in Joomla!'s default article system as a way to lighten up the database from old articles. K2 is better optimized and so it doesn't need that.
Additionally, you can use the K2 Tools module to list K2 content by month created, similar to a blog archive, as it's usually found in such platforms.