Link analyses come into play when you’re concerned about the quality of your overall link profile, and you want to maintain that quality.
If your link profile has minor amounts of bad links, you probably don’t want to care about doing a link analysis, as it’s more work than what you need to maintain.
However, if your link profile contains significant amounts of bad links, and you feel like you are an ongoing target for negative SEO campaigns, you will want to consider a regular link remediation schedule.
Depending on the size of your link profile, this could be once a month or once a quarter.
Sometimes, ongoing link analyses are required to uncover more sophisticated negative SEO campaigns. But it isn’t always necessary and could be overkill for some smaller websites.