Firstly what is a big site? Is it 10.000 pages or 100.000 or even 100.000? My experience is that sites that more than 10 .000 to 15.000 pages start to show the same symptoms, the main problem in most cases is the WCMS (web content management system), how it is used to manage the sites content.
This can be how templates are designed to show and possibly reuse content. Little problems within sites that contain millions of pages can occur again and again and grow from being a minor glitch in being a huge disaster that prevents search visibility.