I had the same problem with CF7 not working; however, I had not made any recent changes. As it was a server side error – I called my host (bluehost) and it turns out I had hit my email limit. They raised the limit and it worked again. It was never a problem with CF7 or wordpress.
So, my suggestion – also consider checking with your web host. Especially if you have not made any recent changes/upgrades.