TButton类型不能响应鼠标双击事件，即使用了显式声明,如:
TxyButton = class(TButton)
published
  property OnDBlClick;
end;

查了一下源代码:
procedure TControl.WMLButtonDblClk(var Message: TWMLButtonDblClk);
begin
  SendCancelMode(Self);
  inherited;
  if csCaptureMouse in ControlStyle then MouseCapture := True;
  if csClickEvents in ControlStyle then DblClick;  //注意这里的csClickEvents
  DoMouseDown(Message, mbLeft, [ssDouble]);
end

实际上TControl的子类默认的ControlStyle都带有csClickEvents的：
constructor TControl.Create(AOwner: TComponent);
begin
  inherited Create(AOwner);
  FWindowProc := WndProc;
  FControlStyle := [csCaptureMouse, csClickEvents, csSetCaption, csDoubleClicks];
  FFont := TFont.Create;
  ...

但是TButton类就没那么好运了：
constructor TButton.Create(AOwner: TComponent);
begin
  inherited Create(AOwner);
  ControlStyle := [csSetCaption, csDoubleClicks];
  //注意这里没有csClickEvents
  Width := 75;
  Height := 25;
  TabStop := True;
end;

解决方法有两种：

一、拦截WM_LButtonDBLCLK

二、在TButton的声明中显式加入csClickEvents

constructor TxyButton.Create;
begin
  inherited Create(Form1);
  ControlStyle := ControlStyle + [csClickEvents];
  OnDBLClick := OnDBClick;
end;

procedure TxyButton.OnDBClick(Sender: TObject);
begin
  ShowMessage('DBClick');
end;