Thanks for your quick help so far!
It is a good find: the success message does work when in the “description”, but not in the short description area. So that seems to be an issue with the form that I’ll raise with the jetpack developers.
For now I can put the text in the short description area, and the form in the other one.
However, the reason I started using the short-description is because in the Trusted theme, the picture is so large, that the description often ends up below the fold (whereas the short description appears next to the picture). Making the picture itself smaller doesn’t seem to work, is there another way to fix this?