The blog was hacked yesterday. All of those blog posts were up for less than an hour and promptly deleted. So I highly doubt they had any impact on the rank.
I 100% agree that this site is ugly and not well formatted. But the client is unwilling to change that or pay for a design. So we have to try to build a house on a bad foundation to begin.
Most pages have header tags
And while I see all of these things as issues, I am more concerned with why the site would rank and then suddenly disappear entirely. Backlinks are obviously a big thing, but it is a small local niche site where I can say that a large portion of the companies also do not have backlinks or even an seo company helping.
The site gets "A" grades on their moz on page reports for keyword targeting so I feel they should at least be somewhere to be found.