How can I programmatically prevent the combobox from dropping

You can avoid the combobox dropping by overriding its WndProc method and ignoring the WM_LBUTTONDOWN and WM_LBUTTONDBLCLK.

[C#]
 public class MyComboBox : ComboBox
 {
	protected override void WndProc(ref System.Windows.Forms.Message m)
	{
		 if(m.Msg == 0x201  //WM_LBUTTONDOWN
		    || m.Msg == 0x203)  //WM_LBUTTONDBLCLK
  			 return;
		base.WndProc(ref m);
	}
 }

[VB.NET]
Public Class MyComboBox
	Inherits ComboBox
   
	Protected Overrides Sub WndProc(ByRef m As System.Windows.Forms.Message)
		If m.Msg = &H201 OrElse m.Msg = &H203 Then ’WM_LBUTTONDOWN  or WM_LBUTTONDBLCLK
			Return
		End If

		MyBase.WndProc(m)
	End Sub ’WndProc
End Class ’MyComboBox