To repeoduce:
- Set the AutoCompleteMode to suggest and paste some text in the drop down list.

Workaround:
protected override void OnLoad(EventArgs e)
{
    base.OnLoad(e);
    radDropDownList1.TextChanged += radDropDownList1_TextChanged;
}
void radDropDownList1_TextChanged(object sender, EventArgs e)
{
    this.radDropDownList1.DropDownListElement.AutoCompleteSuggest.HandleAutoSuggest(this.radDropDownList1.Text);
}