I experienced the same problem ever since I added a password protected page. I have deleted it from each page and have deducted that the password migrates to whatever page I exit from. Create a dummy page, an unlisted page, and use for exiting your website editor. This practice will eliminate that problem with your published site.
Another solution is to delete the password from your browser. Drew will provide instructions when he get to work.
These are his instructions:
If you have a page that has become password protected and you never added the password, then it is because the password has been save in your browser and the browser is adding it to the field. When you save the page and publish, the browser has added the password to the page and it goes online. You will need to enter the password manager of the browser and locate the line for "sitebuilder.homestead.com" and remove it from the list.
Chrome1) Go to Settings and scroll down to the bottom and click Advanced.

2) Scroll down to the Password section and click on Manage passwords

3) Find the Website sitebuilder.homestead.com and remove it.
Firefox1) Open Options and click Security, then Saved Log ins. Then search for sitebuilder.homestead.com and remove it.

This should prevent this from happening again.