Hi @jodzeee
Thanks for sharing your URL, and the screenshot there. That second connection option is there because it is possible to have your site connected to Jetpack, but with a site-only connection. If you connect your WordPress.com account, more Jetpack features are available (features that require user authentication).
In terms of the Jetpack connection on your site, unfortunately it isn’t possible to get notifications when Jetpack is disconnected on your site though this is a feature that may be considered in the future. I do notice that there are quite a lot of active plugins on the site (visible via the Jetpack connection itself), so it is possible that another plugin could be interfering with the connection at times (more likely a security plugin in that case), as Mehdi mentioned. But the best bet here would be to reach out to your host to ask for server error logs from around the times that you notice Jetpack is disconnected. If there is something happening at a hosting level, the logs may pick that up.
Do let us know what you find here and we’ll be happy to troubleshoot further if possible as well.