The submit button in the http://demo.magnolia-cms.com/.magnolia/admincentral#app:pages:detail;/demo-features/modules/public-user-registration/PURUpdate:edit page's content is a 'stkPURAuthSubmit'.
But in the available components of this component '/modules/standard-templating-kit/templates/components/pur/groupFields' it is not available. Only the 'stkPURNotAuthSubmit' is available.

But for the 'PURUpdate' page and the 'password-reset' is the authenticated submit button needed and not the non-authenticated.

Solution:
Add the 'stkPURAuthSubmit' to the availableComponents of the '/modules/standard-templating-kit/templates/components/pur/groupFields' component.