The tab order in the dialog is incorrect, the dialog is not focused when shown.

Workaround: 

public partial class Form1 : Form
{
    public Form1()
    {
        InitializeComponent();

        radRichTextEditor1.RichTextBoxElement.FindReplaceDialog = new MyFindReplaceDialog();

    }
}
class MyFindReplaceDialog : FindReplaceDialog
{
    public MyFindReplaceDialog()
    {
        this.Controls[0].TabIndex = 2; // FindNext button
        this.Controls[1].TabIndex = 3; // Replace Button
        this.Controls[2].TabIndex = 5; // CloseButton
        this.Controls[3].TabIndex = 4; // Replace All button
        //this.Controls[4].TabIndex = 5; // label
        //this.Controls[5].TabIndex = 5; // label
        this.Controls[6].TabIndex = 1; // RepalceWith textbox
        this.Controls[7].TabIndex = 0; // TextToFind  textbox
         

    }
    protected override void OnShown(EventArgs e)
    {
        base.OnShown(e);
        this.Controls[7].Focus();
    }
}