TL;DR:

Don’t do your drawing in response to a one-time UI event with Control.CreateGraphics. Instead, register a Paint event handler for the control on which you want to paint, and do your drawing with the Graphics object passed via the PaintEventArgs.

If you want to paint only after a button click (for example), in your Click handler, set a boolean flag indicating that the button has been clicked and then call Control.Invalidate(). Then do your rendering conditionally in the Paint handler.

Finally, if your control’s contents should change with the size of the control, register a Resize event handler and call Invalidate() there too.

Example code:

private bool _doCustomDrawing = false;

private void drawPanel_Paint(object sender, PaintEventArgs e)
{
    if (_doCustomDrawing)
    {
        Graphics g = e.Graphics;
        g.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.AntiAlias;
        g.Clear(Color.White);
        Size size = drawPanel.ClientSize;
        Rectangle bounds = drawPanel.ClientRectangle;
        bounds.Inflate(-10, -10);
        g.FillEllipse(Brushes.LightGreen, bounds);
        g.DrawEllipse(Pens.Black, bounds);
    }
}

private void drawButton_Click(object sender, EventArgs e)
{
    _doCustomDrawing = true;
    drawPanel.Invalidate();
}

private void drawPanel_Resize(object sender, EventArgs e)
{
    drawPanel.Invalidate();
}

But why? What was I doing wrong, and how does this fix it?

Take a look at the documentation for Control.CreateGraphics:

The Graphics object that you retrieve through the CreateGraphics method should not normally be retained after the current Windows message has been processed, because anything painted with that object will be erased with the next WM_PAINT message.

Windows doesn’t take responsibility for retaining the graphics you draw to your Control. Rather, it identifies situations in which your control will require a repaint and informs it with a WM_PAINT message. Then it’s up to your control to repaint itself. This happens in the OnPaint method, which you can override if you subclass Control or one of its subclasses. If you’re not subclassing, you can still do custom drawing by handling the public Paint event, which a control will fire near the end of its OnPaint method. This is where you want to hook in, to make sure your graphics get redrawn every time the Control is told to repaint. Otherwise, part or all of your control will be painted over to the control’s default appearance.

Repainting happens when all or part of a control is invalidated. You can invalidate the entire control, requesting a full repaint, by calling Control.Invalidate(). Other situations may require only a partial repaint. If Windows determines that only part of a Control needs to be repainted, the PaintEventArgs you receive will have a non-empty ClipRegion. In this situation, your drawing will only affect the area in the ClipRegion, even if you try to draw to areas outside that region. This is why the call to drawPanel.Invalidate() was required in the above example. Because the appearance of drawPanel needs to change with the size of the control and only the new parts of the control are invalidated when the window is expanded, it’s necessary to request a full repaint with each resize.