To reproduce:
- Enter a value in the search row (make sure you will have several results)
- Enter a letter in the filtering row. The filetring row will lose the focus.

Workaround:
public class MyGridViewSearchRowInfo : GridViewSearchRowInfo
{
    public MyGridViewSearchRowInfo(GridViewInfo viewInfo) : base(viewInfo)
    {
    }

    public override void SelectNextSearchResult()
    {
        GridViewSystemRowInfo systemRow = this.ViewTemplate.MasterTemplate.CurrentRow as GridViewSystemRowInfo;

        if (systemRow != null && this.ViewTemplate.MasterTemplate.Owner.EditorManager.IsInEditMode)
        {
            return;
        }
        base.SelectNextSearchResult();
    }
}

//change the default row like this
void radGridView1_CreateRowInfo(object sender, GridViewCreateRowInfoEventArgs e)
{
    if (e.RowInfo is GridViewSearchRowInfo)
    {
        e.RowInfo = new MyGridViewSearchRowInfo(e.ViewInfo);
    }
}