To reproduce:
Setup RadDropDownList as follows:

DataTable parentDataTable = new DataTable();
parentDataTable.Columns.Add("P1", typeof(decimal));
parentDataTable.Columns.Add("P2", typeof(string));

parentDataTable.Rows.Add({
    1,
    "match_at_start"
});
parentDataTable.Rows.Add({
    2,
    "contains_match"
});

dd.DataSource = parentDataTable;

dd.DisplayMember = "P2";

dd.SelectedItem = null;

dd.DropDownStyle = RadDropDownStyle.DropDown;
dd.AutoCompleteMode = AutoCompleteMode.SuggestAppend;
dd.DropDownListElement.AutoCompleteSuggest.SuggestMode = SuggestMode.Contains;

Start the project, type "ma" in the DropDownList, using the arrows select the first item and click tab. Delete the text in the DropDownList and type "ma" again, press the arrow down and you will notice that the text is not being updated.

Workaround:

Handle the KeyUp event: 

this.dd.KeyUp += KeyUp;

private void KeyUp(object sender, KeyEventArgs e)
{
    if (e.KeyCode == Keys.Down || e.KeyCode == Keys.Up) 
{
        if (this.dd.DropDownListElement.Text != this.dd.DropDownListElement.Items(this.dd.DropDownListElement.SelectedIndex).Text) 
{
            this.dd.DropDownListElement.Text = this.dd.DropDownListElement.Items(this.dd.DropDownListElement.SelectedIndex).Text;
        }
    }
}