Did you try disabling all plugins besides Jetpack and trying again? When I had this problem, it turned out that my coming soon page plugin was affecting Jetpack. Once the site itself was finished, as soon as I took it out of coming soon mode everything worked fine.
I get it that maybe at one point JetPack was very useful to have but with new plugins and themes it isn't necessary to have it any longer. I get it however that maybe those who had found it a life saver up to a couple or more years ago, like around 2012/2013 that they still believe in the plugin. Like something one is used to with WordPress and feel comfortable to have around.