Did you ever figure out how to fix this? I am experiencing the same exact thing...
This is a difficult issue to explain so I'll state it as plainly as I can.
I can bring up the Amazon.com homepage. I can sign in. But the moment I click on a object it will log me out automatically. The excemption is the recommendations page. I can click that and stay logged in.
I have toyed around with the internet tools and I made to where my computer will except all cookies after I deleted all browsing history and reentering the site. Still nothing working.
Looking for any advice I can follow.