jQuery stops working in a ahah wrapper div returned as json data
Not really a Drupal question, but the slider is created in Javascript on the document.ready -event which can't as such be triggered manually.

When you fetch a piece of content via ajax to the page, it just replaces the html, but does not attach any event handlers or run any document.ready -code. You need to handle that explicitly.

What I'd do is I'd check out what function EasySlider calls on document.ready and just repeat that call after the ajax content is fetched.