I think netmeg is right on here, you need to figure out what's going on with your visitors to rule out usability issues and see if conversions can be improved. It's time for a new baseline that you can use to measure the impact of new changes over time which will, unfortunately, take months to complete. Make minor changes and watch for effect while allowing sufficient time for those changes to propagate.
Yada, yada, I know you understand what netmeg suggests but I wanted to add a note specifically about your index page. Take a look at your index page from the point of view of a first time visitor.
- Does it very clearly tell a visitor exactly what the site can do for them?
- Does it clearly tell a visitor why they want to bookmark the site and come back regularly?
- Does it signal authority? Quality?
I have seen some sites, mostly built on wordpress, that just display the latest 10 articles and these sites seem to have been impacted more harshly than others. If the index page content is ever changing there needs to be some very strong signals to answer the questions above. Google raters will be looking for these things on your index page every time they are asked to evaluate internal pages.
Lastly, it has to be asked, does this site have many affiliate offers? Sites with a lot of affiliate links don't seem to hold their ground as well with recent changes. They can do well but they require extra effort, the 'more' Google demands has to offset the affiliate link effect, especially if you have pages with a lot of affiliate links(or only affiliate content) on them.
Advertorials are under the gun right now, pages with only advertorial speak AND affiliate links are double in trouble.
If it's not an affiliate site, and you do sell product directly to customers, are your product descriptions unique or repeated from the manufacturer? Duplicate content is not only from scraped pages, it can be from repeated product descriptions.