Hi Alan
Sounds like a bit of a headache. First things first...don't assume all drops etc are negative. Often big drops in search via good SEO are a sign that you might be serviing better content and this must be also compared to other metrics like bounce rates etc.
Domain rank drops can also mean that sites which are also high ranking have been removed, because their links where not related to your content and therefore in the longer term, could be damaging. Remember links should be from sites which are somehow related to your site. Google is striving for better service delivery to all searchers and therefore does not want links from a site selling widgets to be linking to sites selling cakes, unless the widget is something to do with cakes.
Press coverage, tends to have no-follow links and therefore check out the value of a link before spending time trying to get the link.
Domain Authority comes from quality linked content and therefore high ranking links in your industry sector should be sought. Links are like roots, tiny capillary fibres that grow to big anchor roots in time.
Improve your content and make it fresh. This will do wonders for natural links and google serving up your site. Track keywords and distil the essence of your site pages to ensure that not one hit is wasted. I could be wrong but Google also monitors BOUNCE RATE.
Hope that helps somewhat
Bruce