It probably depends on the site. There are some high-authority sites that are basically platforms for other sites, so in that case, no.
I would think a relevant link from an integral but low-authority page on a high-authority site would be a plus, especially because the authority of that page might be higher than you think (maybe Moz just hasn't found its other links yet, for example).
As far as your problem, to start, I'd take a close look at the pages that used to convert and see if there are any on-site improvements you can make. Use the on-page grader and make sure you have your bases covered on that end.