Task manager stays on top, even when "opened" multiple times.

chrome/views/widget_win.cc

 // Copyright (c) 2006-2008 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/views/widget_win.h"
 
 #include "base/gfx/native_theme.h"
 #include "base/string_util.h"
 #include "base/win_util.h"
 #include "chrome/app/chrome_dll_resource.h"
@@ skipping 223 matching lines @@
   ::ClientToScreen(hwnd_, &p);
   out->SetRect(crect.left + p.x, crect.top + p.y,
                crect.Width(), crect.Height());
 }
 
 void WidgetWin::MoveToFront(bool should_activate) {
   int flags = SWP_NOMOVE | SWP_NOSIZE;
   if (!should_activate) {
     flags |= SWP_NOACTIVATE;
   }
-  SetWindowPos(HWND_NOTOPMOST, 0, 0, 0, 0, flags);
+
+  // Check if the window is topmost.
+  WINDOWINFO wi;
+  wi.cbSize = sizeof(WINDOWINFO);
+  GetWindowInfo(GetHWND(), &wi);
+  if ((wi.dwExStyle & WS_EX_TOPMOST) > 0)
+    SetWindowPos(HWND_TOPMOST, 0, 0, 0, 0, flags);
+  else
+    SetWindowPos(HWND_NOTOPMOST, 0, 0, 0, 0, flags);
 }
 
 HWND WidgetWin::GetHWND() const {
   return hwnd_;
 }
 
 void WidgetWin::PaintNow(const gfx::Rect& update_rect) {
   if (use_layered_buffer_) {
     PaintLayeredWindow();
   } else if (root_view_->NeedsPainting(false) && IsWindow()) {
@@ skipping 699 matching lines @@
   if (message == WM_NCDESTROY) {
     TRACK_HWND_DESTRUCTION(window);
     widget->hwnd_ = NULL;
     widget->OnFinalMessage(window);
   }
   return result;
 }
 
 }  // namespace views