How do I prevent updating fields after submission?

I am not sure if I understand your query correctly. Do you mean to restrict the user to edit the submission after submitting the form? If so, I see that there is an Edit link provided in the Autoresponder email that allows the user to edit the submission at anytime later. 

You may remove the edit link from the Autoresponder email to prevent the user to editing the submission later. 

Hope this information helps! Let us know if you are referring something different. We will be happy to help.