Currently, a user must be logged-in to have the ability to save a draft. We have a feature request to allow saving of drafts for logged-out users, and our developers are currently working on a new Form Abandonment add-on that will allow this to work - but in the meantime, there is a simple workaround:

What I would recommend is building two forms. The first will be your user registration form, and should be kept as simple as possible - only the bare minimum of details required to register a user. The form should be set to log the user in automatically when they submit the form, and the text on the submit button should be changed to "Next". The redirect URL should then take users to your main multipage form.

Full details on how to set up the user registration action can be found in our documentation here: https://formidableforms.com/knowledgebase/user-registration/

Using this method, users won't even realize they are being logged-in, and won't notice that these are two separate forms. But they get all the benefits of a logged-in user, like drafts being automatically saved on each page turn.