I have done some testing and it seems that the success message does not display when the form is in the ‘Product short description’ area.
Tested with Trusted and Twenty Seventeen and it does not display with either, although it does when the form is in the main content area (the ‘Description’ section on live product pages).
So, it looks like a possible issue when the form is in the short description area of WooCommerce products.
On our testing site, when trying to add a contact form to the short description section, the ‘Add Contact Form’ button would not add the form to the textarea, so I had to add the form with a [shortcode] using ‘Text’ view. Did you have the same issue?