Mostly that occurs when SEO is done by shorcuts and bypasses not focusing on the quality. Another reason is that external links on website are not blocked by a nofollow command in the script so google algorythm thinks this site is selling links, which will make your ranking drop as well.
1) Tell google not to follow that backlink for any ranking purpose by adding a nofollow command to your script.
2) I propose a 30 days campain of tagging and linking to your website. But it has to comme from clients, influencers and being real
3) being referred by subject from other sites
4) Re-submission of your site on other search engines, less importants but Google algorythm hates the compétition.
I'll be happy to talk to you
Alain Richard