A few years back we ran white-label hosted payment pages: each merchant's own branding, their own domain, our checkout behind it. One morning one of those pages stopped taking cards. Nothing had been deployed, no code had changed. The certificate on that domain had quietly expired overnight, and browsers were refusing to load the page at all.
Nobody was watching that date. The page had worked the day before, so everyone assumed it would work again. We heard about it from a confused customer's support message instead of a monitor, and by then a good part of a business day of card payments on someone else's storefront was simply gone.
These days certificate and domain expiry get monitored the same way we monitor databases and queues: an alert with days of warning, going to the same place as everything else that can take a product down. It's unglamorous, and it sits above design, copy and page speed on our list, because all three of those are useless on a page that won't open.
So if you're checking five things on your website today, start with this one: what gets told before your certificate and your domain renewal lapse. A person's memory is probably not the thing you want there, you want something that will wake someone up.