I have the subscribe button included in the sidebar since a long time.
Now it does not appear on the title page but as soon as I go to a subpage, the button appears as expected. (tested with recent Firefox and Chrome)
There is a javascript issue on your homepage.
Something on the page is breaking the app.js code as you can see in the console (F12 key in your browser)
The first thing I can see is that wp-hide-post plugin is loaded on the home page and not on the other page(s).
maybe you can test deactivating that and see if that helps
It was not the wp-hide-post but the Podlove Subscribe Button plugin.
I did not realize that the subscribe button was integrated into the PPP as a module.