Contact Form: can submit form multiple times using existing Post data

#### Steps to reproduce the issue

1. Start with a Jetpack site with the contact form module active.
2. Create a new page, and add a form. Publish the page.
3. While logged out, submit a form and capture the data posted on submission.
4. Log back in, edit the page, and mark it as password-protected.
5. Log out. Although you can't access the page anymore, you can still submit forms using the data from the last form you submitted. The `contact-form-hash` attached to each submission can be re-used.

Original report: 602506-h1

Start by reproducing the password-protected contact form scenario and trace where the contact-form-hash is accepted during submission. Done means previously captured submission data and its hash can no longer submit a form after the page becomes password-protected; no specific source file or test is named in the issue.

Written by the indexing model from the issue text.