You cannot use RadComboBox's ItemsRequested event, because this makes client page callbacks. During client callbacks, the page does not go through its regular page life cycle and the page content is not updated. Only the caller of the callback receives the callback result. So, even though you have the server-side controls initialized on a page callback, their state is not maintained and the changes are not sent to the client.
If I understand you correctly, you need to implement a search box where the results get dynamically re-updated when the user types. To do that, you need to use RadAjaxManager's client-side object to dynamically initiate AJAX request. Using the manager's server-side AjaxRequest event, you can handle the search operation and update the listview. Note that to setup this scenario, you need to define an AJAX setting where RadAjaxManager updates RadListView.
I have attached a sample test page demonstrating this approach.
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