Webmeister - 6:31 pm on Jun 26, 2010 (gmt 0)
I can guarantee you from the past week's experience that there is. I have a client whose highest traffic page fell from #1 on two big query terms to pages 3 and 4. What they did was change (not tweak, demolish) ALL the body content and the page template. I was not informed ahead of time and I only learned about it after the traffic drop appeared.
Their site uses 6 templates, and they switched the same URL from the existing template to one of the others that they use for new announcements and promotions. They even kept the same title and H1 tags, but they did switch the big Flash movie that heads the page.
Traffic loss? 28,000 to 100. The take-away is this: on-page factors still influence rankings. This internal page still has backlinks at the six figures level with a natural percentage of keyword anchor text.
Did they change the entire site? If so, then they probably changed pages that have links pointing to your home page on them. If that is the case, I believe it was because the internal pages linking to their home page were modified - not because the home page was modified.
If CNN.com changed its template completely, would that kill their #1 ranking for "headline news"? No, because 99% of their backlinks are on other websites, and it wouldn't matter. I'm guessing your client probably trashed pages that affected the majority of their backlinks.