The search statistics is facing a major rework soon, the current state was designed to capture only live result requests. Using google analytics to track search queries is a great alternative – if you are using google analytics, then you can search for “google site search tracking”, there should be a tutorial available for WordPress as well.
Well, do you know which plugins are those exactly (I mean their website or URL to the wordpress.org database)? Maybe I can find a documentation to them.