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This was a panda issue. It's fixed now. We lowered the outbound link count and cleaned up the site as a whole. Traffic is at about 70% of what it was.

I like your answer

...as you go deeper and deeper into the site, the link juice is divided more and more. My question: Is this really true or just a concept? I believe that this is true.  The more internal links you have hitting deep pages the more importance they will receive in google's rankings.  But, in addition to straight linkjuice there is also anchor text value. I don't want to guess and give you a generic answer to your question on what to do.  If this was my site I would be looking at analytics to see where the traffic is coming in and where it is coming from.  Are those deep pages pulling any visitors from the search engines. A more important problem that you might have is thin content.  Lots of your pages have very few words on them.  Some of your categories are empty.  You might have a problem with Google as the recent Panda update is believed to be demoting sites with thin content.   Also, I have found that increasing the content on a page from a few words to a few sentences to a few paragraphs often results in a progressive rankings increase in low competition niches. I have a blog that gets a lot of short posts and we regularly delete a lot of posts and redirect the URLs because they have a lot of value for a short period of time but they are not "evergreen" content (declining traffic).  We do that to conserve linkjuice and to avoid being seen as a site that has a ton of trivial content.

For one, do not use rel=nofollow on any internal links. Matt Cutts has said this in the plainest of language. Don't do it. PageRank sculpting like this does not work. What you describe is true. If your home page has a certain amount of link juice, the more pages in your site and the more links per page will diminish the amount of link juice each page receives, at least from your own pages. You can increase the amount of pagerank of any page with external links. At the end of the day the way you try to funnel around pagerank on your site is almost entirely meaningless. Unless you have a ton of pagerank, you will put in a lot of work redoing your architecture for nothing. Think of your users first and what makes the best user experience. That's the most important. From there, simply get some external links to your most important pages. That's what I would recommend for this.