Keeping an eye on your best inbound links is like monitoring whether or not your best customers are still in the market. Links are the ‘currency’ of search engines, and you don’t want to lose them.
There are two parties who can break the links: you, and the site linking to you. The first is easy to prevent: make sure all the web page addresses (URLs) on your site, past and present, continue to work. Any which have been withdrawn over the years (because you removed pages, or completely redesigned the site), must be ‘301 redirected’ to a relevant, working current page. It’s never too late to do this.
I’ve heard of a company going back to its Google Analytics ‘top pages’ report from seven or eight years ago, finding dozens of pages there which no longer existed and which hadn’t been redirected, and fixing that by adding a redirection. The research is actually quite an easy exercise, and we’d be happy to do it for any of our clients for free. The result can be the restoration of a whole bunch of external links from sites you might have forgotten about years ago, or never even knew about.
Fixing things where the other party has broken the link is harder, and requires knowing who links to you. There are many backlink checkers out there, such as the tool at Moz.com, but one of the simplest is the “Links to your site” report at Google Search Console. You can also see the sites which are sending you traffic through Google Analytics*.
I like to download a list once a year, and check if any links have been lost in the previous 12 months. Then it’s a case of finding out why, and – if appropriate – contacting the linking site to see if the link can be restored, perhaps by providing some updated information.
*Acquisition > Referrals > (Click on the site name)