The article, Why Your Search Rankings Are Dropping (and 7 Ways to Fix It) by Neil Patel goes through seven reasons you might be losing rankings on Google that you have worked so hard to gain, as well as how to remedy those issues.
It should be noted that this article ignores the fact that you might be losing rank because of a bad online reputation. If you are finding bad content/bad links pointing to your site, you should look into online reputation management as that can be a hard mess to clean up.
Some of the most common problems (with the simplest solutions) are site speed (your site is too slow), out of date content (you need to update your web page), and internal linking (you need to link between pages on your own site. Obviously getting the content on your web page up to date, and keeping it relevant for the keywords that you want to rank for is the quickest and easiest fix. This also helps when there is bad news about your company on the internet and you want to rank good news above it to push down negative search results (see more tips in link).
Internal linking can be relatively simple for a small site, and very hard for a large site. The best way to go about this is by finding content words and phrases on your site that is relevant to other content and linking those words and phrases to that content. You can also start creating content with internal links in mind.
Site speed can be a little trickier, but it can definitely help you regain rankings. The article has some great suggestions on improving your site speed.
Some of the other methods the article covers are link building, click-through rate, design, and social shares. All of these methods can be a little harder to manage because they are out of your control. One interesting tidbit is that you do not want to build links to the page that is losing rank because Google can spot when a page is getting links at an unnatural rate. Instead you want to improve your domain authority by building links that link to that page internally.
I would add that the primary reason, outside of what is mentioned in this article that a site or page might be losing rank is because you have a negative reputation and it may be time for some crisis communication. If that is the case for you, look into online reputation management.