I had the same problem and found that it interfered with some of the other plugins I had installed. Deactivate the other plugins and activate them one at a time and you may find one or more that break the Custom Contact Forms admin page.
I would also like to do this. I have to use the contact 7 plug in for this when Custom contact makes the forms too long.
I have the same issue. I have 9 fields on my forms and if I wish to change one I have to delete the subsequent fields first, then add them back in. It also takes about 12 button clicks to add and save a field to a form. This could be a one click add field to form button, and the order should be set with an scroll, arrow, or priority number.