Jetpack is notoriously unreliable at testing your website's uptime and availability. If you have their uptime monitoring turned on, it's likely you'll receive lots of false positive emails about your website being down when it's not. There are dozens of threads about this online, and sadly the suggested reasons are rarely the case in our experience - their monitoring is simply very buggy! Although the vast majority of Jetpack's downtime emails are false positives, two classic signatures to watch out for are where Jetpack is claiming extremely long periods of downtime (i.e. more than an hour), or a lot of small instances of downtime (for example that your site was down for a few minutes, multiple times). These are always problems with Jetpack's reporting and not your website being down.
If you see an email from them at the time, you can check your website itself to see it's online. If you don't see their email until later, you can contact our support team with the date and time of the reported downtime. We will check the access logs for your website and confirm if there were people and crawlers happily browsing your website at the same time Jetpack was claiming it was down. (In some cases, we've even seen Jetpack happily browsing the site with an "everything's normal" 200 code yet still reporting it as down!)
After that, we recommend you do the following: Log in to your WordPress Dashboard as normal. Click "Jetpack" in your sidebar. Under the "Security" settings tab, toggle off "Get alerts if your site goes offline." and save your changes. This will save your sanity and your inbox! (Or if you don't know why you have Jetpack, you can likely uninstall it completely, which will also improve your site performance. Feel free to get in touch with our support team and they'll let you know if you need to use it, and what features you can replace with better free plugins if needed)
