repeater control binding fully recreates all of children controls inside repeater templates. Because new DataBind result may (or may not) contains extremely different data inside repeater. What kind of controls and their state you want to maintain inside repeater? Maybe using ordinal html controls and operating with theirs through Request.Form collection would be a better way?
If you want to save data from repeater before applying new databinding, best place for making it is a Page.PreRender event. In this event all Page controls already recreated and their viewstate already restored. So you may iterate by Repeater.Items collection and save data from repeater row by row. And after saving all the data you may rebind repeater controls according current filter values from page.