There are a number of posts about getting jQuery controls to work around update panels, the most notable being http://stackoverflow.com/questions/1106029/asp-net-jquery-autocomplete-textbox-not-responding-after-first-search, but I haven't been able to find anything discussing the behavior that I'm seeing.
I've been able to rebind the auto-completer to the text fields using both the pageLoad javascript function and by putting the $(document).ready() call in a script manager in the page_load server side event. The problem is, after certain update panel calls the auto-completer no longer selects the first element after a successful lookup.
Generally, I wouldn't really have a problem with this, the user can still use the arrows or the mouse to select the element they want and everything works correctly, but if an element isn't selected and they press the return key the overlay window closes and they are left on the main screen with the orphaned auto-completer that has nothing to do with the current page.