Hi @lellojello,
Thanks for reaching out. From inspecting your site I can see that both the secure (https) and the non secure (http) versions of your site are accessible. In addition, from checking your public REST endpoints it looks like you may have mismatching URLs defined within your WordPress configurations, one with http and the other https.
In such cases it’s not unexpected to become disconnected, as Site Kit uses only one version of your site to connect with and display information from. If you, as a site administrator, happen to access the non connected version, the plugin will recognize a site URL change.
Luckily there is an easy solution to this. Firstly you can define both URLs as fully secure (https), from your WordPress general settings screen (Settings > General). As your website has a valid security certificate this will also ensure your traffic is fully https. Note that if Site Kit is currently connected to the http version of your site, you may be asked to reconnect once more, at which point you should remain connected.
You may then also wish to ensure all non secure traffic to your site is always secure you can use a plugin, or setup a http > https redirect at host level.
Let me know if you need any assistance with the above. I’m also happy to check that your website is only accessibly via https once you make the changes above.