To reproduce:

public Form1()
{
    InitializeComponent();

    this.radTextBox1.Multiline = true;
    this.radTextBox1.Size = new Size(200, 200);
    this.radTextBox1.TextChanged += radTextBox1_TextChanged;
}

private void radTextBox1_TextChanged(object sender, EventArgs e)
{
    this.radTextBox1.BackColor = Color.Red;
}

Note: when you keep pressed a specific key, you will notice that the memory consumption is increased, although if you force the GarbageCollector, it is released. It is also noticeable that there is text lagging while typing. Please refer to the attached gif file.

Workaround:
            this.radTextBox1.TextBoxElement.TextBoxItem.TextBoxControl.BackColor = Color.Red;