I can't see the specifics of your set up, so let me make a couple of observations.
First: if you have a field in the form that you want to save so that it can later be displayed you should probably go ahead and create and assign such a custom field with Types, rather than using generic fields with "persist": 1.
Second: Types custom fields use a wpcf- prefix for the post meta key, whereas if you add a generic field with "persist":1 it will get saved with the slug of the field as the post meta key, without such a prefix.
If you believe that the generic field is not getting saved, you should verify this in the only place that you can tell for sure, i.e. in the database. Check the wp_postmeta table corresponding to the post in question, and confirm which custom fields have been saved.