Could you go to your client's site, and check the Feedbacks menu in the dashboard? Are the Feedbacks stored there?
If they are, the problem is most likely caused by an issue with the server's email settings. Unfortunately, I won't be able to help you with that, but your client's hosting provider should be able to help.
If Feedbacks do not appear in the Feedbacks menu, the problem could be caused by a conflict with another plugin. Could you try to deactivate all other plugins, one at a time, and let me know if one of them conflicts with Jetpack Contact forms?