tedster - 5:44 am on Apr 3, 2010 (gmt 0)
If this website is as strong as Zappos, then maybe you can get away with a lot of links from the home page. But as far as I know, Zappos isn't struggling with a continuous decline in Google traffic - in fact they are wildly successul and I am sure they see a lot more that 1600 search visits a week for their domain name.
A strong information architecture takes hard work, but it sure does serve a website well. Still, the decline in traffic that you're describing is apparently recent, so the home page links probably aren't the actual cause.
If the site name is referring less traffic, it could mean many things. Does the site rank #1 for its own name?
And a second possibility -- does this site have unique content, or is its information duplicated on other sites?