Hey, I have exactly the same problem with the plug. I strongly need help on this. Currently I use the plugin that generates a replacement form, but lack the ability to add new form fields is terribly problematic.
For me the problem with the plug Contact Form 7 occurred about 1.5 months ago, but also came to this lack of choice and to add new form fields to the right in the administration panel.
I ask your help in this matter, I am in great need of this plugin.