Rectangle drawn always is erased when the next is created

When the form's client area is invalidated the entire surface is marked for redrawing. The next time OnPaint is called, what is painted is what is in the event handler. You draw one rectangle and so you see one.

You need to accumulate the information related to the rectangles you need to draw. Then in the paint handler, you can refer to the information and draw them all.

Below example is the slightly modified version of the code in the question. It substitutes a TQueue of rectangles in the place of unused integer variables (pos1, pos2..). A rectangle is queued and any excess rectangle is dequeued when mouse the button is released. Maximum number of recalled rectangles is defined by a constant. The paint handler enumerates the queue to draw the rectangles.

uses
  ..., generics.collections;

type
  TForm1 = class(TForm)
    procedure FormMouseDown(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer);
    procedure FormMouseMove(Sender: TObject; Shift: TShiftState; X, Y: Integer);
    procedure FormMouseUp(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer);
    procedure FormPaint(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure FormDestroy(Sender: TObject);
  private
    FSelecting: Boolean;
    FSelection: TRect;
    FRectangles: TQueue<TRect>;
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

const
  MAXRECTANGLECOUNT = 2;

procedure TForm1.FormCreate(Sender: TObject);
begin
  FRectangles := TQueue<TRect>.Create;
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
  FRectangles.Free;
end;

procedure TForm1.FormMouseDown(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer);
begin
  FSelection.Left := X;
  FSelection.Top := Y;
  FSelecting := true;
end;

procedure TForm1.FormMouseMove(Sender: TObject; Shift: TShiftState; X, Y: Integer);
begin
  if FSelecting then
  begin
    FSelection.Right := X;
    FSelection.Bottom := Y;
    Invalidate;
  end;
end;

procedure TForm1.FormMouseUp(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer);
begin
  FSelecting := false;
  FSelection.Right := X;
  FSelection.Bottom := Y;
  Invalidate;

  FSelection.NormalizeRect;
  if not FSelection.IsEmpty then
  begin
    FRectangles.Enqueue(FSelection);
    if FRectangles.Count > MAXRECTANGLECOUNT then
      FRectangles.Dequeue;
  end;
end;

procedure TForm1.FormPaint(Sender: TObject);
var
  R: TRect;
begin
  Canvas.Brush.Style := bsClear;
  Canvas.Pen.Style := psSolid;
  Canvas.Pen.Color := clRed;
  Canvas.Rectangle(FSelection);

  for R in FRectangles do
    Canvas.Rectangle(R);
end;

end.