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We worked with a content site years ago that focused mostly on superhero movie news and a lot of their traffic came from Google News. One day it just dried up and dropped by more than 90%. They brought us on to help and what we figured out was they were feeding Google their sponsored posts for months. The posts were made to look like news but were very clearly sponsorships pushing product so they got hit with a penalty. Not sure if that is what is going on with you but it's food for thought. As Tom mentioned, they are very volatile channels.

Why take the risk? Having your site load with the www doesn't hurt you. It's not as if the site will perform better without the www and if your site is configured properly your site will load no matter how you have that part of it set.

Google views www.domain.com as a different site from domain.com. You can mitgiate your risk by doing 301 redirects from your www site to your non www but there is always going to be some amount of risk and the potential to see a temporary dip while Google figures out what just happened. Not sure I see enough benefit in making the move to warrant changing it.

Google will view it as one site so you shouldn't have any issues from that perspective. The Google bot is just looking at pages and won't know/care that the underlying CMS that is running some pages is a different install than other pages. The downside is you now have two websites to maintain, two themes, two sets of files, etc... That may result in a bit of a headache in the future.