One of the WordPress plugins that I find most useful for my site is the Broken Link Checker. It will email me if its scan of my blog posts finds any links that are broken or unresponsive.
The former category can either be replaced with a copy from the Internet Archive (which the plugin can find for me automagically), or removed if no copy is available and the post updated to explain the change. In a few cases, I've had to remove posts because the loss of the link rendered them meaningless, but thankfully that has been rare so far.
More concerning to me are the cases of links that are persistently unresponsive, or throw up other errors. YouTube is a notable culprit, possibly because Google doesn't like its video service being probed in this away. A few other sites that repeatedly crop up with timeouts or no access may be under attack. (I won't name them, for obvious reasons.) For those, I've switched over to Internet Archive copies of the linked pages. Or perhaps the server is struggling due to lack of resources? I wish I knew the cause, but for now, I either mark them 'not broken' and hope for the best, or mark them 'dismiss' and wait to see if their status changes.
(There is a third category, not normally reported to me by email — links which have been redirected. Sometimes, this is due to sites' policies regarding geolocation and GDPR, but in a few cases the redirect is because the site has been acquired or shut down. I have to check these manually a few times a week.)