CellTable with custom Header containing SearchBox and Focus Problem

I am trying to implement a CellTable with a custom Column Header which displays a SearchBox (simple Textbox) below the normal Column text.
The SearchBox should allow the user to filter the CellTable. It should look something like this:

  |Header  1|Header 2 |
  |SEARCHBOX|SEARCHBOX|
  -------------------------------------------------------
  |    ROW 1 
  ------------------------------------------------------
  |    ROW 2 

As soon as the user types in a character into the SearchBox a RangeChangeEvent is fired which leads to a server requests and the CellTable is updated with the new filtered list.

Basically everything works fine. However as soon as the CellTable is refreshed the SearchBox loses its focus and the user has to click with the mouse into the SearchBox again to type in a new character.

This is probably related to the fact that the render method of the custom header and its cell is called after the CellTable refresh.
Is there any way how to set the focus back to the SearchBox? I tried to set tabindex=0 but it didn't help.

Custom Header Class

public static class SearchHeader extends Header<SearchTerm> {
    @Override
    public void render(Context context, SafeHtmlBuilder sb) {
        super.render(context, sb);
    }
    private SearchTerm searchTerm;
    public SearchHeader(SearchTerm searchTerm,ValueUpdater<SearchTerm> valueUpdater) {
        super(new SearchCell());
        setUpdater(valueUpdater);
        this.searchTerm = searchTerm;
    }
    @Override
    public SearchTerm getValue() {
        return searchTerm;
    }
 }

Custom Search Cell (used in the custom Header)

The isChanged boolean flag is set to true when the user types something into the SearchBox and is set back to false if the SearchBox loses its focus. I