To reproduce:
private void radButton1_Click(object sender, EventArgs e)
{
    radGridView1.MasterView.TableSearchRow.SelectNextSearchResult();

}
Check the index in the search textbox, it is not updated. 

Workaround:
var cell = radGridView1.TableElement.FindDescendant<GridSearchCellElement>();
if (cell != null)
{
    cell.FindNextButton.PerformClick();
}