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Whether a subdomain carries all the weight of the main domain has yet to be proven, but I think in this case it does. But link equity flows from the page not the domain. A better test is: does the site look spammy? Do I want my brand on there? If yes, awesome. Then: Did I pay for this placement? (If yes, please rethink that unless it's advertising and nofollowed) If it's natural and good for your brand, no matter what site, just keep it there.

This could change in traffic be soooo many things without knowing your site's entire background. There could be a Panda/Penguin penalty in play (I have no way of knowing) so read up on those and make sure you're not a victim of duplicate/thin content and/or shady link building practices (even if they occurred in the past, use OSE to take a look). I'm not seeing the redirect from non www to www as an issue in terms of ranking but double check that you implemented that correctly.  I haven't heard of losing rankings over this tweak before but I suppose it's possible that it takes Google a some time to figure that out (though I dont see why it would hurt rankings in the interim). Other sites outranking you for your own article is actually quite common if you're not on a strong domain otherwise.  3rd page sounds rather harsh though.  Are you engaging in any questionable link building practices? Without knowing more it's really tough to say what your site's problem might be.  I think I can rule out the 301 redirect from www to non-www if implimented correctly.  Sean is correct in checking your robots.txt file as well. Hope I answered your question if not solving your greater problem for you!

Thanks Andriy.  They are all do-follow links.  I will put less focus on trying to get links with keywords as anchors.