Its difficult to diagnose without seeing code. You may need to add Page.EnableViewState = true; or it could be that you need to re-populate the listbox on postback.
If you want to be able to plug a feature into a CMS page it needs to be a UserControl, it is not possible to embed on page inside another page and cms pages already have a page. It is possible to plug in physical .aspx pages but it is not the recommended approach there are drawbacks to doing that.