Here’s a workaround (it’s a bit ugly though).
In your LookAndFeel override preparePopupMenuWindow and re-add the MenuWindow to the desktop, without the windowIgnoresKeyPresses flag:
void MyLookAndFeel::preparePopupMenuWindow(Component& window)
{
if (!window.getParentComponent())
window.addToDesktop(ComponentPeer::windowIsTemporary | getMenuWindowFlags());
}
