Hi!
I believe this is rather an issue with the cache plugin, because Ajax Search Pro cannot affect the caching method in any ways.
I’ve logged in, cleared the cache, currently I can see the ajax search pro search bar in the header on every page I have checked. Ther might be a browser cache header as well, so it is possible that your browser serves the cached page files. It should expire within few days, but you can try reloading the page by hitting the CTRL + SHIFT + R buttons. That usually works.